Substitution Definition and 816 Threads

I've been doing Calculus examples using substitution recently, and some are very easy to spot when to make what u, but sometimes it's not that easy. I'm having trouble determining which equations I should make as u, and which ones I shouldn't. I would greatly appreciate it if I could be given...

Homework Statement indefinite integral 5\picos\pit Homework Equations The Attempt at a Solution 5\pi int cos\pit Substitution Method 5\pi x sin (1/\pit

Homework Statement integral of 1/(x^2 + z^2)^(3/2) dx, where z is a constant Homework Equations The Attempt at a Solution I set u = arctan(x/z) so du = z/(x^2 + z^2) dx but now I'm honestly stuck.

Homework Statement integral of (2/(sqrt.(1-t^2))dt evaluated at sqrt.3 / 2 and root 2 / 2. Homework Equations none The Attempt at a Solution i believe its just substition. u=t^3 du=3t^2 1/3 du = t^2 then you get 2/3(1/sqrt(1-u^2))dt

Homework Statement This may be basic, but how do you know which part of an integration problem fill the up the triangle values for trig substitution?

i don;t have a specific homework question. i have a sort of conceptual question instead when integrating by substitution, how do i know what to choose as u? for example integral of z^2 / (1 + z^3)^(1/3) dz i am suppposed to choose u as 1+z^3. any other value for u won't give me the...

Homework Statement Integral of dx/[(x2 - 2x + 2)2]Homework Equations Trig substitution rules: for expression sqrt(a2 - x2) make x = asin(t) with -(pi/2) < t < (pi/2) for sqrt(x2 - a2) make x = asec(t) with 0< t < (pi/2) and for sqrt(a2 + x2) make x = atan(t) with -(pi/2) < t < (pi/2)The...

\int x^{2} \sqrt{4+x^{2}} dx I've already subbed in: x = 2tan\theta dx = 2sec^{2}\theta d\theta and I've gotten down to: 16 \int tan^{3}\theta sec^{3}\theta d\theta But now I have noo idea what to do! Can someone give me a hint?

Homework Statement Integrate: 6/(1+sqrt(7x))dxHomework Equations the hint was that u^2=7x The Attempt at a Solution by substituting u, i got the antiderivative of (12/7)(u/(1+u))du so i substituted again and ended up getting 12/7(1+sqrt(7x)-ln(sqrt(7x)+1)) but apparently that's wrong. please...

Homework Statement Show that if A is a tautology, then so is *(A). A is a well formed formula, * is a function that replaces all sentence symbols A_1, A_2, etc. with formulas B_1, B_2, etc. , respectively Homework Equations * is defined recursively, starting with the fact that if A_n is...

Homework Statement dy/dx=a^2/(x+y)^2 where a is a constant need the answer in the form x=f(y) Homework Equations The Attempt at a Solution multiplying out (x+y)^2 gives dy/dx=a^2/(x^2+2xy+y^2) setting u=y/x dy/dx can be rewritten as dy/dx=a^2/((x^2)*(u+1)^2)...

Homework Statement t^2 y' + 4ty - y^3 = 0 Homework Equations Hint was given in the question: substitute with v = y^-2 The Attempt at a Solution Dividing by t^2 and isolating y': t^2 y' = y^3 - 4ty y' = y^3 / t^2 - 4y/t dv/dt = 0 y = v^(-1/2) dy/dt = (-1/2)v^(-3/2) v' so...

Homework Statement Integrate: \sqrt{x}e^\sqrt{x}Homework Equations See aboveThe Attempt at a Solution Well I started off first by taking t=sqrt(x) but that didn't get me very far. So then I decided to make x equal to t^2 which sort of worked. After hours of struggle I decided to have a look at...

I noticed that there are some functions that when integrated by substitution, are incorrect. Such as (1-x^2)^(-1/2). The answer is obviously arcsinx, but if you integrate with substitution, set u = 1-x^2, du = -2x dx. Then use anti power rule to go from u^(-.5) to 2u^(.5), then divide by -2x...

Homework Statement Evaluate the integral. Int((x+5)(x-5)^(1/3)dxHomework Equations The Attempt at a Solution I've attempted the problem but subsitution doesn't seem to do anything, as du = dx if u = x-5, which doesn't cancel anything.

Homework Statement Well, i didn't know how to do anti-derivatives on this forum so i just did it on paint :) Anyways, here is the problem and solution i tried. Let me know if i did anything wrong, or if i even did anything right... Thanks a lot! i have to find the anti derivative of ...

Homework Statement Indefinite Integral (x^3)sqrt((x^2)+4)dx Homework Equations With an x= 2tan@ and dx= 2 (sec^2)@ d@ The Attempt at a Solution I get to 8(tan^3)@(sqrt((4tan^2)@+(8sec^2)@d@ Simplified down to 8(tan^3)@(sqrt((12tan^2)@+8d@ After that I'm stuck The...

Only a substitution product is obtained when the compound below is treated with sodium methoxide. Draw the substitution product and explain why an elimination product is not obtained (If the image doesn't show up, the compound is 1-bromo-2,6-dimethylcyclohexane)Homework Equations - The...

Homework Statement [PLAIN]http://img293.imageshack.us/img293/5026/solutoni.png Hi all, Can anyone explain what is going on where? I understand that it is a different way of writing the conventional integration by substitution, instead of using the symbol u. The second line, however...

Homework Statement Intergrate: \int\frac{3 dx}{\left(2-x\right)^{2}} By substituion. Homework Equations n/a The Attempt at a Solution Ok so first I take the integer out to get: 3\cdot\int\frac{dx}{\left(2-x\right)^{2}} Now I let u = 2 - x and du = dx to get...

In a differential equation in doing a substitution such as z=dy/dx can I do the following:zdx=dy Integrate both sides y=zx

Homework Statement I uploaded a picture of a question in OWL. What I don't understand is, how to tell when I should take into account cis-trans products. For example, in the question I uploaded, why does chlorine add as cis and trans in right two images, but does not add cis and trans to the...

Homework Statement \int_0^1 \! 7x\sqrt{x^2+4} dxHomework Equations The Attempt at a Solution Noticing that the radical is of the form x^2 + a^2, I know to use a*tan\theta. x = 2tan\theta dx = 2sec^2\theta d\thetaThen I simplified the radical to put it in terms of a trig function...

Homework Statement \int \frac{4}{x^{2}\sqrt{81-x^{2}}} dx Homework Equations The Attempt at a Solution Since the radical is of the form a^2-x^2, I'm using the substitution x=asin\theta. x = 9sin\theta dx = 9cos\theta d\theta Using this x value, I solved the radical...

I am trying to figure out which substitution to use to get this integral done: \int \frac{du}{\sqrt{u-u^2} \cdot (1+ub)} When I plug it into Mathematica I get: \sqrt{\frac{4}{b+1}} \cdot \texttt{arctan} \left ( \sqrt{\frac{(b+1)u}{1-u}} \right ) Any ideas about a suitable substitution?

Homework Statement Starting from the Gamma function: \Gamma (s) = \int^{\infty}_{0} dx \, x^{s-1} e^{-x} Make a change of variable to express it in the form: \Gamma (s) = f(s) \int^{\infty}_{0} dy \, \exp{\frac{-A(y)}{\zeta(s)}} And identify the functions f(s), A(y)...

Here's the equation: ∫(sqrt(2),2) (1/(x^3*sqrt(x^2 - 1)) I have the entire indefinite integral worked down to this (using x = a*secø): ø/2 + 1/4 * sin2ø Now I have the answer book, so I know that's right so far. What I don't understand is how it converted the points of the integral...

Homework Statement lim t^2-9/t-3 x>3 Homework Equations The Attempt at a Solution I factored it into (t-3)(t+3)/(t-3) i then canceled out the (t-3)'s and substituted 3 to get 6 is this correct?

Homework Statement evaluate: higher limit of 36 lower limit of 0 (36+3x)^1/2 dx Homework Equations i thought of using subsititution? The Attempt at a Solution g(x)=36+3x g'(x)=3 when x=0, u=36+3(0)=36 when x=36, u=36+3(36)=144 from lower limit of 36 to higher...

I have attached a word document that shows all the work and equations. Your help is appreciated.

Homework Statement I'm not even going to get to the real problem. I'm just having a basic mental block with how to do the substitution. I just need to know how to convert this ODE into terms of zHomework Equations x^2y''+xy'+4(x^4-1)y = 0 x^2 = zThe Attempt at a Solution I have some vague...

Trigonometric substitution - Why? Hey guys Im sitting here with trigonometric substitution problems, and I have a kind of a problem. I can't see WHY it is legal to substitute x for a sin (\theta) If you have a the integral: \int\frac{1}{\sqrt{1-x^2}}dx Then I know the substitution would...

Hi everyone, This question is a bit involved but it pertains to calculating the differential of a variable substitution used in the proof of the convolution theorem (http://en.wikipedia.org/wiki/Convolution_theorem) Consider \int f(t) \int g(s - t) ds dt. If we use the substitution...

Hi, I am seeking some input for an integral I have been stumped on for a few days. This is the integral: [(a^2 - s^2)^1/2]/(x-s) ds evaluated over the bounds from -a to a. The symmetry of the integration area allows the integral to be evaluated from 0 to a, and doubled. I have always...

I am to prove something inductively. Can one substitute as follows? For the inductive part, assume that (*) n_k < n_(k+1) In order to show that this implies: (**) n_(k+1) < n_(k+2), Can one then simply make the substitution k+1 = s in (**), yielding n_(s) < n_(s+1)?

Homework Statement Substitute an electron in a neutral hydrogen atom with a muon. a) calculate the Bohr radius of the ground state for this myonic atom of atom. The answer must be right to at least 2 significant digits. b) Calculate the fraction of the myon that is located inside the proton...

Homework Statement Substitute an electron in a neutral hydrogen atom with a muon. a) calculate the Bohr radius of the ground state for this myonic atom of atom. The answer must be right to at least 2 significant digits. b) Calculate the fraction of the myon that is located inside the proton...

Hey. I am having a hard time solving this problem. (x^2)y' + 2xy = 5y^4 I get as far as simplifying to y' = [(5y^4)/(x^2)] - 2y/x Then use v: y/x and y: vx & y': v'x + v And get v'x + v = [5(v^4)(x^2)] - 2v And then I get lost. Any help would be appreciated. Thanks!

Homework Statement Find the general solution to the boundary value problem. Homework Equations (xy')' + \lambda x^{-1}y = 0 y(1) = 0 y(e) = 0 use x = e^t The Attempt at a Solution x = e^t so \frac{dx}{dt} = e^t using chain rule: y' = e^{-t}\frac{dy}{dt} Substituting...

Homework Statement y'=y+y^3 Homework Equations The Attempt at a Solution I set y=v, dy/dx = dv/dx. Substituted back into original equation ST dv/dx = v + v^3. Cross multiply, then divide yielded dv/(v+v^3) = dx. After that, I have no clue. The book gives the following...

Hi, I am developing a Ultrasound application where the sensor will be in contact with the skin but I can't use gel for accoustic coupling (or any liquid). Any ideas of materials (suppliers) for this purpose ? Thanks/Brgds Joao

Homework Statement By using the substitution t = tan x, find \int \frac{dx}{\cos^2 x+4\sin^2 x} Homework Equations The Attempt at a Solution Well let tan x=t \frac{dt}{dx}=\sec^2 x=\tan^2 x+1=1+t^2 the integral then becomes \int...

1. Homework Statement ∫√(4-x^2)/x dx 2. Homework Equations 3. The Attempt at a Solution a^2=4 u^2=x^2 ⇒ u=asinθ a=2 u=x x=2sinθ sinθ 2cosθ=√(4-x^2) dx=2cosθ dθ ∫√(4-4sin^2θ)/2sinθ 2cosθ dθ ∫2cos^2θ/2sinθ 2cosθ dθ 2∫cos^2θ/sinθ cosθ dθ Now what? I have been working...

Homework Statement ∫√(4-x^2)/x dx Homework Equations The Attempt at a Solution a^2=4 u^2=x^2 ⇒ u=asinθ a=2 u=x x=2sinθ sinθ=x/2 (Our professor uses a triangle method which I won't draw) 2cosθ=√(4-x^2) dx=2cosθ dθ ∫√(4-x^2)/x dx=∫2cosθ/2sinθ dθ...

(Apologies for not following the template for topic creation, but I wasn't sure how to adapt my problem to fit it). I'm following the derivation of the spherical harmonics in section 3.3 of Rae's "Quantum Mechanics", but have come across a step I can't quite understand. It seems like such a...

xdy/dx+y=1/y^2:using substitution in differential eq Homework Statement solve using substitution xdy/dx+y=1/y^2 The Attempt at a Solution Thanks to the people who've help me thus far. here's a bernulli problem that I'm having. I change this problem around to... dy/dx=y^3/xy^2...

Hello! This is a quick question more to do with understanding. When using a sine substitution in an integral, such as: \int \sqrt{a^2-x^2} dx Using the substitution x = a sin{t} Don't you 'lose' some information? Because the range of values for x can be from neg. inf. to pos...

Homework Statement \int2x^3/2x^2+1 Homework Equations None The Attempt at a Solution I used substitution u = 2x^2+1 du/dt = 4x dt = du/4x \int(2x^3/u)du/4x cancel out the x to get \int(2x^2/u)du/4 solve for 2x^2 u = 2x^2 + 1 2x^2 = u - 1 \int((u-1)/u)du/4...

Homework Statement I started the problem, got stuck. Homework Equations The Attempt at a Solution

Homework Statement Please explain how to use the substitution rule in indefinite integrals. I am unable even to start the problem. Homework Equations The Attempt at a Solution