Substitution Definition and 816 Threads

A substitution reaction (also known as single displacement reaction or single substitution reaction) is a chemical reaction during which one functional group in a chemical compound is replaced by another functional group. Substitution reactions are of prime importance in organic chemistry. Substitution reactions in organic chemistry are classified either as electrophilic or nucleophilic depending upon the reagent involved, whether a reactive intermediate involved in the reaction is a carbocation, a carbanion or a free radical, and whether the substrate is aliphatic or aromatic. Detailed understanding of a reaction type helps to predict the product outcome in a reaction. It also is helpful for optimizing a reaction with regard to variables such as temperature and choice of solvent.
A good example of a substitution reaction is halogenation. When chlorine gas (Cl2) is irradiated, some of the molecules are split into two chlorine radicals (Cl•) whose free electrons are strongly nucleophilic. One of them breaks a C–H covalent bond in CH4 and grabs the hydrogen atom to form the electrically neutral HCl. The other radical reforms a covalent bond with the CH3• to form CH3Cl (methyl chloride).

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  1. MathematicalPhysicist

    A question in substitution in logic.

    i need to prove that if x is the first of sub(\phi;a,\psi) then there exists 1<=i<=n and there exist firsts \phi' of \phi_i and \psi' for \psi such that x=sub(\phi';a,\psi)\psi' where sub(t;a,b) is defined as follows: let a1,..,an be n signs and b1,..,bn expressions. a=(a1,...,an)...
  2. S

    Solving Trig Substitution: \int cos^2x tan^3xdx

    How would I go about solving this: \int cos^2x tan^3xdx..all i did so far .. \int cos^2x tanx(tan^2x) [[ \frac{1}{cosx}^2 -1] = tan^2x so... \int cos^2x[[ \frac{1}{cosx}]^2-1]tanx is this right so far...now what?
  3. S

    Substitution homework question

    Hi, I am having a little bit of trouble with the following: \int sintsec^2(cost)dt heres what I have so far u=cost du=-sintdt -\int sec^2(u)du -2tan(u) + C is this right?
  4. W

    Help with Diff EQ Integrals Using Trig Substitution

    I am working on a Differential Equation problem and I am stuck on these two integrals: http://forums.cramster.com/Answer-Board/Image/cramster-equation-20064101738436328028752372062504976.gif and...
  5. G01

    Integral t = tan(x/2) substitution

    \int \frac{dx}{5 - 3\sin x + 4 cos x} I know I have to use t = tan(x/2) substitution, and after i do that and symplify I get: \int \frac{dt}{2t^2 - 3t + 1} I don't know where to go from here. If anyone can see where to go, please help. Also, if there is an easier way to do this, please...
  6. D

    Help with substitution of cosh(A),etc, into equation

    Hi there, I was given this equation, cosh(A+B)=cos(A).cosh(B) + sinh(A).sinh(B) then I was told to write down the definition of cosh(A+B) which I did. But then I'm told to substitue the defintions of cosh(A), sinh(A), cosh(B) and sinh(B) into the right hand side of the equation, and to...
  7. W

    How do you use substitution to solve integrals involving x, u, and n?

    Qn. By using a suitable substituition, find \int{\frac{1}{x\sqrt{1+x^n}}dx} I haven't encountered this specific type of question before, so I went to use the obvious substitution u^2=1+x^n, getting: 2u=n x^{n-1} \frac{dx}{du}\Leftrightarrow \frac{dx}{du}=\frac{2u}{n} x^{1-n} Hence...
  8. S

    Impulse and Momentum: Substitution Trouble

    Ok, in this problem I am getting bogged down in the basic algebra part of it. I had one person explain it once but I still missed something.:frown: a 1055-kg van, stopped at a traffic light, is hit directly in the rear by a 715-kg car traveling with a velocity of +2.26 m/s. Assume that the...
  9. J

    Integrating with Substitution: Solving Tricky Integrals

    Am i being really dumb when struggling to do this? L = 4\sqrt{2}c \left \int_{0}^{\frac{\pi}{2}} \left \frac{dt}{\sqrt{1 + sin^2 t}} Using substitution or otherwise show that L = 4c \left \int_{0}^{1} \left \frac{du}{\sqrt{1 - u^4}} Its a small part of a question but its stopping me...
  10. Hootenanny

    Can you spot the error in this integration by substitution problem?

    The question is to find the following intergal: \int x\cdot u^{\frac{1}{2} where u = 2x -1. = \int x\cdot u^{\frac{1}{2}} \;\; \frac{1}{2} du u = 2x -1 \Rightarrow x = \frac{u+1}{2} = \int \frac{1}{2}(u+1)\cdot u^{\frac{1}{2}} \;\; \frac{1}{2} du \;\; = \int \frac{1}{4}\left(...
  11. B

    Use substitution x=2tan(y) to integrate (37dx)/(x^2*sqrt(x^2+4)) in y

    I feel so :cry: doing this problem. PLEASE HELP! AND TEACH ME How TO DO IT. My question is this. use the substitution x=2tan(y) (37dx)/(x^2*sqrt(x^2+4)) give the answer in terms of y. I did the substition, but it looked more complicated. It doesn't look like a u*du thing, but it...
  12. O

    What is the Integral of e^(-bx^2) Using Substitution?

    Hello! I've got a problem I've been working on for hours. I get a clue; If the integral (from zero to infinity) of e^(-x^2) is sqrt(pi)/2, what is the integral (from zero to infinity) of e^(-bx^2)? I've tried substitution, but I kind of got it wrong. If x = y/sqrt(b), I get the same...
  13. H

    Solving differential equations using substitution

    Solve the differential equation by making an appropriate substitution x^2dy=(xy+x^2e^\frac{y}{x}) Here was my first attempt: Let y=ux, dy=udx+xdu x^2(udx+xdu)=(ux^2+x^2e^\frac{ux}{x})dx x^2(udx+xdu)=(ux^2+x^2e^u)dx x^2udx+x^3du=x^2udx+x^2dx+e^udx x^3du=x^2dx+e^udx And after...
  14. S

    with Trig Substitution Integration

    I am not too good with trig identities. I can't seem to figure out how to simplify these trig intergrals. I know I can use a triangle to turn the second problem into a trig integral, but once I have the trig integral, I am lost. Any help would be greatly appriciated.:redface...
  15. S

    Solving an Integral: Finding the Substitution

    Ok, apparently it's been a while since I've had to deal with an integral like this, seems like it should be easy but I can't find a substitution that will work. The integral is: \int_{0}^{h}\frac{dx}{(x^2+R^2)^\left1/2\right} Where R is a constant. Any hints (or solutions if you're...
  16. T

    Integration of 1/x^2 sqrt(16-x) with substitution

    my question is integra 1 / x^2 sqr root(16-x^2) i use x = 4 sin y then i got to integrate 1/16 times [1/(sin y)^2] in which i got stuck.pls help...how do i continue from there as i not sure ow to integra 1/(siny^2
  17. S

    Trig sine substitution doesnt work

    how would on integrate \int_{0}^{1} \sqrt{1 + 4t^2} dt trig sub sittution doesn't work since one doesn't get tan^2 +1 . i tryed solving this with matematica and it yielded something with a sinh argument. I am not familiarwi the hyp sine substitution.
  18. P

    Integrating 1/sqrt(x^2 + y^2 + z^2) Using Trig Substitution: A Physics Problem

    On this physics problem i need to do a double integral (dx,dy) of 1/sqrt(x^2 + y^2 +z^2). Which looks easy enough at first, until I reallized (after many hours) I cannot figure out how to integrate it. I am sure at this point there is some trig substitution (learned too long ago...), but I am...
  19. B

    When is the Best Time to Use Trig Substitution?

    When is th ebest time to use it and what are some good rules of thumb for it?
  20. B

    Trouble Solving an Integral: 2tan(u) Substitution

    calc/integral question having trouble with this question int[1/((x^2+4)^2) and i make a trig substitution x=2tan(u) and it seems to get harder with that but its suppose to be it..
  21. quasar987

    How Does Gaussian Wave Packet Transformation Work in Quantum Mechanics?

    Yes, it's me and the wave packets... again! This is taken from the text of Gasiorowicz's Quantum Physics 3rd ed. pp.26. We have a gaussian wave packet at t=0 that is is described by \psi(x,0)=\int_{-\infty}^{\infty}dke^{-\alpha (k-k_0)^2/2}e^{ikx} and we apply the change of variable...
  22. T

    How Do You Compute Derivatives in Spherical Coordinates Using the Chain Rule?

    Let f: \Re^3 \rightarrow \Re be differentiable. Making the substitution x = \rho \cos{\theta} \sin{\phi}, y = \rho \sin{\theta} \sin{\phi}, z = \rho \cos{\phi} (spherical coordinates) into f(x,y,z), compute (partially) df/d(rho), df/d(theta), and df/d(phi) in terms of df/dx, df/dy...
  23. D

    Integral Substitution: Can We Factor in Derivatives to Make Integration Easier?

    Integral Substitution... Heya people, I was wondering if someone here could point me in the right direction, as the book I am reading on Integration isn't very thourough, and I don't really have anyone else to ask. :confused: Basically, I am reading up on u-substitiution regarding...
  24. C

    Solve S (x+5)½/x-4 dx with Substitution Method

    Hi, I have another problem about substitution Method. I think this method is used to make the problem to solve in easy way but it is making my procedure too long for this problem. Can you solve it by substitution method. S (x+5)½/x-4 dx where S is the sign of integral. The answer of...
  25. H

    Finding an antiderivative using substitution rule

    I'm trying to find the antiderivative of [sec(2x)tan(2x)], I can't figure out what part I should be substituting. Any help is appreciated. Thanks, hk
  26. G

    How to integrate int (x^2 + 4)^(-1/2) dx Is it a substitution?

    I need help antidiffing this equation: (x^2+4)^(-1/2) i have tried subbing u=x^2+4 i have tried subbing u= (x^2+4)^(-1/2). i have tried making x the subject. even tried to use partial fraction, with no avail, because i could not figure out how to use partially factorize it. If anyone could...
  27. C

    Is Trigonometric Substitution Needed for ∫ √9-2(x-1)²?

    hi guys im debating whether this question requires trignometric substitution or just normal substitution. ∫ √9-2(x-1)² Im leaning towards normal substitution, with u = x-1, but I am not sure Any ideas Thanx heaps
  28. G

    How Do I Integrate (x^2 + 7x + 10) / (x + 2)?

    how can i integrate: x^2+7x+10 dx x+2 i assume it's by substitution, but i can't work it out. sorry for the formatting, btw
  29. M

    Integration by trig. substitution

    Hello everyone I have an exam tomorrow and I would really appreciate if someone could tell me what I did wrong with this exercice. I did it on paper and I scanned it. Here is the link to the scan: The answer in the book is sqrt(x^2 + x +5/4) + 2ln(sqrt(x^2 + 2x + 2) + x +1) + C...
  30. N

    Simple Integral w/ Trigonometric Substitution

    Hello everyone, I am having some trouble with an integral. \int \sqrt{x^2 - 1} dx so far: x = sec \theta \frac{dx}{d \theta} = sec \theta tan \theta dx = sec \theta tan \theta d\theta now we substitute: \int \sqrt{x^2 - 1} dx = \int \sqrt{sec^2 \theta - 1} sec \theta tan...
  31. P

    How do I use trig substitution to solve this integral?

    im hoping i worked this out right; its long: \int x(81-x^2)^{5/2}dx the integral contains a^2-x^2, so i set x=asin\theta. that would make x=9sin\theta and dx=9cos\theta d\theta: \int 9sin\theta(81-81sin^2\theta)^{5/2}9cos\theta d\theta = \int 9sin\theta[81(1-sin^2\theta)]^{5/2}9cos\theta...
  32. M

    Got a question with substitution?

    Using the Substitution method, find the maximum value of 4x-2xy+3y subject to the constraint 4x-y=2 I can do the 1st part: 4x-y=2---> 4x-2=y substitute this into the original equation: 4x-2x(4x-2)+3(4x-2) Hope that right so far! but don't know where to go from there? anyone...
  33. E

    Substitution Methods for 1st Order Diff. Eqns - Help for Beginners

    Hi, I'm new to the forum, and new to differential equations. I was wondering if someone could post a no-nonsence explanation of substitution methods for first order differential equations. Thanks!
  34. A

    Special relativity and substitution

    i don't understand when to use substitution as used in the answer to this question: how fast must a pion be moving, on average, to travel 10m before it decays? average lifetime is 2.6*10^-8. i know the answer is D=V( to/ sqroot 1-v^2/c^2) but i don't understand why and how to know when...
  35. A

    How Do You Integrate Using Trigonometric Substitution?

    \int x^3\sqrt{4-9x^2}dx I tried to use x=\frac{2}{3}\cos{(x)} but it just left me with \int \sin^3{(x)}\cos^2{(x)}dx Any suggestions? Thanks for your help.
  36. RadiationX

    Trig substitution help (easy one )

    Use trig substitution to find \int_{0}^{5} \frac{dt}{25 + x^2}dt I can solve it to here \int_{0}^{\frac{\pi}{4}}\frac{25sec^2\theta}{(25 + tan^2\theta)^2} and from this point i can factor the denominator into {625(1+ \tan^2\theta)}^2 which becomes 625\sec^4\theta now i have the...
  37. T

    Integration question - use of substitution

    Hi, I have to find this one: \int \frac{dx}{\sqrt{1-e^{2x}}} Is this right approach? \int \frac{dx}{\sqrt{1-e^{2x}}} = \int \frac{e^{2x} dx}{e^{2x} \sqrt{1-e^{2x}}} Substitution: t = \sqrt{1-e^{2x}} dt = - \frac{e^{2x}}{\sqrt{1-e^{2x}}} dx e^{2x} = 1 -...
  38. I

    Double Integral Substitution: Solving for the Jacobian in Terms of u and v

    The question is Evaluate the double integral over the region R of the function f(x,y)=(x/y -y/x), where R is in the first quadrant, bounded by the curves xy=1, xy=3, x^2 -y^2 =1, x^2-y^2 =4. Now it seems that a substitution would be the best bet. What I've done is make u=xy, and v=x^2...
  39. fstam2

    Integration by substitution help

    I am going crazy on this problem: \int sec(v+(\pi/2)) tan(v+\pi/2)) dv if I substitute u= tan(v+\pi/2)) dv , can I use the product rule to find du= sec(v+(\pi/2)) dv . Thanks, Todd
  40. P

    Solving a Trig Substitution Problem: Incorrect Solution

    can someone help me find a appropriate trig sub for this problem: \int\frac{x}{sqrt(-29-4x^2-24x)} took out sqrt(4)... sqrt(4)*sqrt(-29/4-x^2-6x) (i also changed all the negative signs to positive) complete the square... sqrt(4)*sqrt((x+3)^2-7/4) so my trig sub should be...
  41. P

    Problem with math integral substitution

    \int \frac{1}{4x+7*sqrt(x)} what would be a good u substituion for this problem? i can't think of any at the moment
  42. U

    How to Solve an Integration Substitution Problem?

    \int \frac {cos(\sqrt{x})}{\sqrt{x}}dx =? Here's what I did: = \int x^{-0.5}cosx^{0.5}dx subsitute: u= cos(\sqrt{x}) du=-sin(\sqrt{x})(0.5x^{-0.5})dx -\frac {1}{0.5sin(\sqrt{x})}\int u du -\frac{2}{sin(\sqrt{x})} 0.5cos^2(\sqrt{x}) -\frac{1}{sin(\sqrt{x})}cos^2(\sqrt{x}) I know I...
  43. D

    Electrophilic Aromatic Substitution: NO2 & NO Groups

    The NO2 group directs meta with-deactivation in electrophilic aromatic substitution. The nitroso group - NO directs ortho-para with - deactivation. Write out the electroinc structures of - NO2 and -NO and explain the differences in behavior. Show all pertinent resonance forms for the addition of...
  44. P

    Integral: Trig Substitution for 3x^2-1

    Consider the definite integral \int \frac{(x^3)}{(sqrt(3x^2-1))} can someone help me find the appropriate subsitution? i know that i will need this subsitution: sqrt(x^2-a^2) is equal to x=a*sec(theta) well... i have to make 3x^2 look like x^2 somehow. i tried using u-du sub...
  45. V

    About the substitution reaction

    for carbanions, for carbocations and for carbon-centred radicals, does increasing the number of alkyl substituents stabilise or destabilise the intermediate? and why so? :confused: :confused:
  46. R

    Cant solve diff-eq with substitution

    Use subs y=xv to show that (x^2+y^2)+2xy\frac{dy}{dx}=0, x>0 is x^3+3xy^2=k where k is a constant. I played around with this at school and if memory serves me correct i got something similar to \frac{dx}{dv}=\frac{-3}{2xv}-\frac{1}{2} and after that i decided i wasnt on the right path and...
  47. B

    What is an effective variable substitution for solving this integral?

    Hi guys, could someone just suggest a variable substitution for me...just to get the ball rolling : \int_{-1}^{1} \sqrt{1-x^2} - x^2 (\sqrt{1-x^2}) - (1-x^2)^\frac{3}{2} dx Whenever I've seen \sqrt{1-x^2} (and its usually the reciprocal of), I've used trig substitutions to wind...
  48. T

    Trig Substitution with Integration

    How would you go about solving \int \frac{\sqrt{1-x^2}}{x^2} ? I have tried a few things... drawing out triangles... etc but can't seem to get it... I am kind of behind in math because I was gone for awhile because of being sick and presentations.
  49. B

    HHow do I solve this integral using substitution?

    I'm stuck on how to advance further on this problem and if anyone can point my in the right direction I would be greatly appreciative. \int\frac{dx}{\sqrt{x(1-x)}} The integral has to be solved using substitution, but we are required to use u=\sqrt{x} From this...
  50. C

    Why is du/dx treated as a fraction in integration by substitution?

    Integration by substitution... Accroding to my notes, when performing integration by substitution, du/dx= f'(x), and therefore du = f'(x)*dx. But how is this possible? We are treatnig dy/dx as if it were a fraction - but in essence it is not! So why is this statement still true? Thanks. :smile:
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