Substitution Definition and 797 Threads

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...

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

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...