Substitution Definition and 816 Threads

Homework Statement ((x^2)+1)^2 integrate using substitution Homework Equations 3. The attempt at solution ok so i let u= x^2 + 1 du/dx = 2x du= 2xdx where do i go from there

Homework Statement Find any points of intersection of the graphs by the method of substitution. xy+x-2y+3=0 x^2+4y^2-9=0 Homework Equations The Attempt at a Solution From the second equation I can solve for y: y=\frac{\sqrt{9-x^2}}{2} Plug it into the first equation and...

Homework Statement I don't know how to solve these. How do you evaluate the integral of \frac{3dx}{\sqrt{3+X^2}}? I know you have to set x=atan\theta. our a is \sqrt{3} so x =\sqrt{3}tan\theta. That means dx=\sqrt{3}sec2\thetad\theta. I also made a right triangle using the information...

Homework Statement the problem is INTEGRAL 6dz/(z^2(sqrt(z^2+9)) z^2+ a^2 , then z=a*tan@ where a here is 3, because 3^2=9 , i use @ here to represent theta substituting this for z; Int[6/(z^2(sqrt(z^2+9))]dz= Int[(6*3sec^2@d@)/(9tan^2@(sqrt(9tan^2@+9))]=...

Hi there, I am having difficulty with one aspect of intergration by substitution where the substituion of a square root is U^2, wondering if anyone can help. Problem: Integral of: 2x√(3x-4) dx by substituting U^2 = 3x-4 Would du^2/dx = 3 therefore 1/3 du^2 = dx (I think...

double integral to single by "magic" substitution Hi, I have a double (actually quadruple, but the other dimensions don't matter here) integral which looks like this: \iint_0^\infty \frac{d^2 k}{k^2} Now, someone here told me to replace that with \int_0^\infty \frac{1}{2} 2\pi...

Homework Statement d2y/dx2-dy/dx+y*exp(2x) = x*exp(2x)-1 substitute t=exp(x) and set z(t)=y(x) and rewrite hence find all solutions The Attempt at a Solution Rewriting gives: d2z/dt2-dz/dt+z*t^2=(ln(t) * t^2) - 1 however I don't see how this in any way helps us...

Homework Statement By means of substitution x=X+1, y=Y+2 ,shwo that the equation dy/dx=(2x-y)/(x+2y+5) can be reduced to dY/dX=(2X-Y)/(X+2Y).Hence, find the general solution of the given equation. Homework Equations The Attempt at a Solution The first part is quite simple to...

Homework Statement The statement says: Calculate the next integrals using the adequate trigonometric substitution: \displaystyle\int_{}^{}x^2\sqrt[ ]{x^2+3}dxHomework Equations ch^2(t)-sh^2(t)=1\Rightarrow{ch(t)=\sqrt[ ]{1+sh^2(t)}}The Attempt at a Solution x=\sqrt[ ]{3}sh(t) dx=\sqrt[...

Homework Statement Well, the exercise asks me to solve the next integral using an adequate substitution. \displaystyle\int_{}^{}\sqrt[ ]{4-x^2}dx The Attempt at a Solution \displaystyle\int_{}^{}\sqrt[ ]{4-x^2}dx What I did was: x=2\sin\theta dx=2\cos\theta d\theta So, then I get...

Homework Statement Hi there. I'm dealing with undefined integrals now. And I found this one that I don't know how to solve. The problem statement says: Solve the next integrals using the substitution method. \displaystyle\int_{}^{}\displaystyle\frac{\cos(x)}{\sin^3(x)}The Attempt at a Solution...

Hi, I've been doing some additional maths papers and I've seen the use of the substitution u=tan(x/2) in order to calculate integrals. In the mark scheme it states that this particular substitution used to be fairly common, however is not on the modern A-level syllabus. Would someone...

Homework Statement \int \frac{3x}{2x+3} u = 2x +3 x = \frac{1}{2}(u-3} ) dx = \frac{1}{2} du so now the integral should be, \int \frac{ \frac{3u-9}{2}}{u} \times \frac{1}{2} du = \frac{1}{2} \int \frac{3u-9}{2} \times \frac{1}{u} du \frac{1}{2} \int...

I'm attempting to solve the following problem: \int_{0}^{\infty} {\frac{x arctan(x)}{(1+x^{2})^{2}}dx} I started with a substitution: u=arctan(x), du=\frac{1}{(1+x^{2})}dx This seemed like the right thing to do, but after trying to put it together in several different ways I got...

This problem looks relatively simple, but the coefficient in front of the variable is causing issues: \int{\sqrt{1-4x^{2}}}dx So I started like this: x=sin(\theta) dx=cos(\theta)d\theta \int{\sqrt{1-4sin^{2}(\theta)}cos(\theta)d\theta} Normally you can remove the constant from the root and...

Homework Statement If f is continuous and \int^{9}_{0}f(x)dx = 4, find \int^{3}_{0}xf(x^{2})dx Homework Equations None required The Attempt at a Solution Don't really know where to begin, but I tried: for \int^{3}_{0}xf(x^{2})dx let: u = x^{2} du = 2xdx substitute...

Hey All, First post, hopefully it will be readable. I was going to try and word it correctly, but I might as well just post a problem I am having with a certain notation. Take integral of e^6x. Easy enough question. Using U substitution: u = 6x du/dx = 6 du = 6 dx Integral above...

Homework Statement Evaluate ∫ -2 to 2 (x + 3)(4 - x^2)^1/2 dx by writing it as a sum of 2 integrals and interpreting one of those integrals in terms of an area. Homework Equations None. The Attempt at a Solution ∫ -2 to 2 (x + 3)(4 - x^2)^1/2 dx = ∫ 0 to -2 (x + 3)(4 - x^2)^1/2...

Homework Statement Substitute p = \frac{dx}{dt} to solve x\prime\prime + \omega^2x = 0 Homework Equations \frac{dp}{dx} = v + x\frac{dv}{dx} v = \frac{p}{x} The Attempt at a Solution p = \frac{dx}{dt}, \frac{dp}{dt} = \frac{d^2x}{dt^2} \frac{dp}{dt} = \frac{dp}{dx}\frac{dx}{dt} =...

integral of x/(x2+2x+2)dx first thing i did was complete the square to get x/((x+1)2+1 i tried then having x+1 = tanx but that didnt work out because of the x on top i can't just set w = x+1 what would the right substitution be? any hints or help would be appreciated

Homework Statement ∫〖e^√x/√x dx〗 would this be a u substitution or a substitution by parts? Homework Equations The Attempt at a Solution

Homework Statement Using the u substutituion u = 2x + 1, ∫(2x + 1)1/2dx (when x goes from 0 to 2) is equivalent to? Answer: (1/2)*∫(u)1/2du (when x goes from 1 to 5) Homework Equations The Attempt at a Solution If u is 2x + 1, then du = 2dx. Thus, I get (1/2)*∫(u)1/2du...

Homework Statement Evaluate \int\frac{e^t}{\sqrt{e^2^t+9}} Homework Equations N/A The Attempt at a Solution i'm using substitution tan \theta = \frac{e^t}{3} or i also can use tan \theta = \frac{3}{e^t} both will get the same answer. am i right? because my...

Homework Statement 2. The attempt at a solution I

1. Evaluate the integral [0,ln(3)] of ff(x)=(e^2x + 1)^2 /e^x I am having trouble locating what to substitute.

Homework Statement I'm reading a book where they do the following steps which I don't understand: We have a DE: b^2 * y'' = axy put t = b^(-2/3) a ^(1/3) x then somehow get (d^2 y)/dt^2 = ty how? Homework Equations None. The Attempt at a Solution I tried messing with chain...

Homework Statement Hi, \int \frac{1}{x(x^{2}+1)}dx Homework Equations The Attempt at a Solution well I split this into partial fractions \frac{A}{x} + \frac{Bx + C}{x^{2} + 1} so 1 \equiv A(x^{2}+1) + (Bx + C)x when x = 0, A =1 when x = 1, Bx + C = -1 so...

Homework Statement By making the substituion t = \sqrt{1-x} find \int \frac{1}{2 + \sqrt{1 - x}}Homework Equations The Attempt at a Solution So t = (1-x)^\frac{1/2} t' = - \frac{1}{2} (1 - x)^{-\frac{1}{2}} dx = -2 \sqrt{1-x} dt \int \frac{-2 \sqrt{1-x}}{2 + \sqrt{1-x}} dt \int...

Hi, am I on the right track with this U-substitution problem? Homework Statement Evaluate the indefinite integral Homework Equations integral of x^2(x^3 + 5)^9 dx The Attempt at a Solution integral of x^2(x^3 + 5)^9 dx Let u = x^3 + 5 du = 2x^2 1/2du = x^2 1/2 integral u^9 du 1/2...

Homework Statement Evaluate the integral. 1|0 s|0 ( t . sqrt ( t2 + s2 ) dt dsI hope the way I've written it makes some sort of sense. The Attempt at a Solution After getting my head around changing the order of integration I get hit with this question and for some reason am totally...

Homework Statement \int{\frac{x^{3}}{\sqrt{4 - x^{2}}}} NOTE: The use of "0" is theta. I couldn't figure out how to insert one :\ Homework Equations The trig identity sin^{2}0 = 1 - cos^{2}0. The Attempt at a Solution I thought I completed the problem fine, but I realized WolframAlpha has a...

\int\frac{x}{\sqrt{x^2+x+1}}dx \int \frac{x}{\sqrt{(x+\frac{1}{2})^2+\frac{3}{4}}}dx u=x+\frac{1}{2} \int \frac{u-\frac{1}{2}}{\sqrt{u^2+\frac{3}{4}}}du u=\frac{\sqrt{3}}{2}tanT du=\frac{\sqrt{3}}{2}sec^2TdT \int...

In my literature reviews I found a few things that I can't quite understand. Homework Statement I have the following equation: http://img717.yfrog.com/img717/6416/31771570.jpg I'm told that by using the eigenvalue factorization: http://img89.yfrog.com/img89/760/83769756.jpg , I can...

9x^2-4y^2=36 \frac{x^2}{4}-\frac{y^2}{9}=1 y=\frac{3}{2}\sqrt{x^2-4} 3\int_{2}^{3}\sqrt{x^2-4}dx x=2sect dx=2secttant 12\int_{a}^{b}tan^2tsectdt 12\int_{a}^{b}(sec^2t-1)(sect)dt 12\int sec^3tdt-12\int sectdt 6\int secttant-6\int ln|sect+tant|...

To find the integral of the sec(x), you have to substitute a term that is not immediately obvious. \int sec(x) dx = \int sec(x) \frac{sec(x)+tan(x)}{sec(x)+tan(x)} dx u= sec(x)+tan(x) du= (sec(x)tan(x)+sec^{2}(x))dx \int sec(x) \frac{sec(x)+tan(x)}{sec(x)+tan(x)} dx = \int...

Hello! I was looking into haloalkane reactions and the factors which determine the proportion of nucleophilic substitution to elimination reactions. I read that ethanol is more conducive to elimination reactions than substitution reactions, it mentions it being less polar than water, which...

Homework Statement Question is:Integrate x(2x+1)^8 dx in terms of x. Homework Equations The Attempt at a Solution Here is how i started off:by relabeling them. let u = 2x+1. du/dx = 2. dx=du/2. Also x=u-1/2. So my terms now are: Integral (u-1/2)u^8 (du/2) <- this is where i...

\int\frac{x}{x-6}dx u=x-6 \int \frac{u+6}{u}du \int 1+\frac{6}{u} du u+6ln|u|+C x-6+6ln|x-6|+C this appears to be incorrect although it seems logical, also if somone could please tell me the syntax for the definte integral also similar case here \int \frac{x^2}{x+4}dx...

Homework Statement \int(x^5\sqrt{x^2+4})dx The answer is given as: =105(x^2+4)^\frac{3}{2}(15x^4-48x^2+128)+C Homework Equations The Attempt at a Solution u=\sqrt{x^2+4} u^2=x^2+4 2udu=2xdx udu=xdx u^2-4=x^2 \int(x^5\sqrt{x^2+4})dx = \int(u^2+4)^2u^2du =...

Hi, I need to integrate the following: \int \frac{x^2}{\sqrt{9-x^2}} So let x = 3sin\theta \frac{dx}{d\theta} = 3cos\theta So i now have the integral of \frac{9sin^2\theta \cdot 3cos\theta}{3cos\theta} How do i go about the integration from here? parts?

Homework Statement Let R be the smaller of the two regions enclosed by the elipse 144 x2+64 y2=9216 and the line $ x=(8 \sqrt{2})/2$. Find the area of the region R. Homework Equations The Attempt at a Solution my textbook doesn't have anything like this.. i have no idea where...

Hi Everyone! I just need some guidance on this problem. I seem to have trouble what integration technique I need to use on integrals of this type. Homework Statement integrate 1/(25-x^2) Homework Equations sqrt(a^2-u^2) arcsin(u/a) The Attempt at a Solution Would I be...

Homework Statement evaluate using substitution Integral [cos^-1 x]/sqrt[1-x^2] dx Homework Equations The Attempt at a Solution I am just starting with integration and I am getting frustrated with this problem. If someone could show me how to setup and start this problem so I could...

http://img708.imageshack.us/img708/8897/symimage.gif so I did x=atanΘ. which is x=3tanΘ and dx is 3sec^2\Theta. Then it is \sqrt[]{9tan^2\Theta+9}*3sec^2\Theta which evaluates after factoring to \sqrt[]{9sec^2\Theta}*3sec^2\Theta which is then 3sec\Theta*3sec^2\Theta If i take the 9...

Homework Statement \int \frac{\sqrt{196 x^2-144}}{x} dx Homework Equations The Attempt at a Solution I first rewrote the integral... \int \frac{\sqrt{(14x)^2-12^2}}{x} dx Then I let... 14x=12sec\theta thus... x=6/7sec\theta dx=6/7sec \theta tan \theta d \theta My...

Allow me to explain my new theory, The "Mancini conjecture." Ok...lets say I have an integral like (4-x^2)^(1/2) dx. and letting u = 4-x^2, we get du/dx = -2x, and if I took the second derivative of du/dx...i would get -2 this would be ideal, because I would then have du'' = -2 dx, or -1/2...

Homework Statement The answer is: The Attempt at a Solution I tried trig substitution, letting x =\sqrt{2}tan(\theta) and using the identity 1+tan^{2}=sec^{2}(\theta), but couldn't get to the answer. Thanks for the help.

Homework Statement evaluate the integral using the indicated trig substitution. sketch the corresponding right triangle. integral of(1/(x^2 sqrt(x^2 - 9)) Homework Equations integral of(1/(x^2 sqrt(x^2 - 9)) The Attempt at a Solution at first glance this seemed really easy...

Homework Statement \int\sqrt{X^2+1}dX Homework Equations The Attempt at a Solution I used the substitution X=tan \theta So, dX=(sec^2 \theta) d\theta Substituting in for X, I get: \int\sqrt{(tan^2 \theta)+1}(sec^2 \theta) d\theta = \int\sqrt{(sec^2 \theta)}(sec^2...

Homework Statement \int\arctan(4t)dt Homework Equations The Attempt at a Solution \int\arctan(4t)dt = t\arctan(4t) -4 \int \frac{t}{1+16t^2}dt I'm stuck at this point. I think I need to make a substitution for the denominator, but I'm not sure how to go about doing so.