Substitution Definition and 797 Threads

Hey there This is a trig substitution for my Calculus 2 class and I really have NO idea how to get started... \int\frac{4}{\sqrt{3-2x^2}}dx My professor has yet to go over how to evaluate trigonometric substitutions with coefficients in front of variables.

Make an appropriate substitution to find a solution of the equation dy/dx=sin(x-y). Does this general solution contain the linear solution y(x)=x-pi/2 that is readily verified by substitution in the differential equation? Here's what I did: v=x-y y=x-v y'=1-dv/dx 1-dv/dx=sin(v)...

Homework Statement \left( {x + y} \right)y' = x - y Homework Equations Back of book: x^2 - 2xy - y^2 = C The Attempt at a Solution I'm not sure how to start this problem. In the examples in the book, they make a substitution, v=something, and all that was left were v's and...

Homework Statement how do i integrate v^2 / v^2 + 4 Homework Equations i understand this has something to do with arctan but if i use u substitution to let v=(u/2) so (on the bottom) it becomes (1/4)(1+(v/2)^2) there's still a v^2 on the top which the u substitution does not...

Homework Statement It's been god knows how long since I've had to use integration by substitution. I've totally forgotten it. I am trying to integrate to solve for the value of an electric field at a given point. The integral I am trying to solve is...

Homework Statement By direct substitution, show that equation (3) is a solution of the differential equation (2). Homework Equations (2) (d^2 θ)/(dt^2 )=-g/l θ (Second derivative of θ(t)=-g/l θ.) (3) θ(t)=θ_0 cos⁡(√(g/l) t) The Attempt at a Solution I...

Homework Statement Evaluate the indefinite integral... \int x^2 (x^3+5)^9 dx Homework Equations \int f(g(x))g'(x)dx = \int f(u)du The Attempt at a Solution u = x^3+5 du = x^2dx So my answer is... Does that look right? And one more... Homework Statement Evaluate the indefinite...

Homework Statement Using trigonometric substitution, verify that \int \sqrt{a^2[-t^2}dt (INTEGRAL FROM 0 TO \pi)=(1/2)a^2sin^{-1}(x/a)+(1/2)x\sqrt{a^2-x^2 Sorry it doesn't seem to want to allow me to place superscript inside a square root. but inside the first sq. root is a2-t2 and the...

Homework Statement \intsin3cos2xdx The Attempt at a Solution I've successfully solved this problem by factoring out 1 sinx and changing the sin2x to (1-cos2x then assigning u=cosx and du=-sinx and so on. What I'm wondering is why does letting u=sin3x in the original integral not...

Homework Statement Use the appropriate substitution to solve the following D.E.: -ydx + (x + \sqrt{}xy)dy = 0 Homework Equations y = ux The Attempt at a Solution y = ux implies dy = udx + xdu so -xudx + (x + x\sqrt{}u)(udx + xdu) =0 we then get after some simplificaion...

Homework Statement If a and b are positive numbers, show that \int_0^1 x^a*(1-x)^b\,dx = \int_0^1 x^b*(1-x)^a\,dx using only U substitution.Homework Equations Just U substitution and the given equation--I can't use multiplication rules or anything like that; otherwise it would be easy.The...

Differential Equation w/ Homogeneous Coefficients - y=ux substitution I am teaching myself, this problem is from ODEs by Tenenbaum and Pollard. This is not homework for a class. Homework Statement (x+y){dx} - (x-y){dy} = 0 Homework Equations y=ux, {dy} = u{dx} + x{du} The...

Homework Statement \int\int\int _E\(x^2y}\;dV Where E is the solid bounded by x^2/a^2+y^2/b^2+z^2/c^2=1 Homework Equations variable substitution x=au, y=bv, z=cw. The Attempt at a Solution I found the jacobian (abc) and I substituted my variables but I can't find the limits of...

I need to find Lim (x->0) arcsin(2x)/arcsin(3x) I can do a substitution arcsin(2x) = y => 2x = sin(y) and get arcsin(sin(y)) for the nominator, which is equal to y. However, for the denominator i get arcsin(3/2 sin(y)) which I'm not sure what to do with. Am I on the right path?

I am staring at an integral of the form \int \frac{sin(at)}{(1 + bsin^{2}(at))^{1/2}} dt which I have generated for myself (in attempting to model the behaviour of a particle in an oscillating field). I can't see a sensible substitution to try, at present. I could hunt down a standard...

Homework Statement I have recurrence relation problem and what to ask would my way be just as correct as the TA did the solution: f(n) = 0, n=1 and 2f(n/2) + n -1 The Attempt at a Solution Here we assume n = 2k This is my way: f(k-1) = 2[2f(2k-2)*2k-1-1] + 2k - 1 =...

Homework Statement f(n) = 0 when n=1 and 2f(n/2) + n - 1 when n is otherwise Homework Equations Repeated substitution The Attempt at a Solution f(n) = 2f(n/2) + n - 1 = 22f(n/22) + n - 3 = 23f(n/23) + n - 7 = 24f(n/24) + n - 15 Guess: f(n) = 2kf(n/2k) + n...

Hello, I have been wokring on this problem for some hours now, and I get the wrong answer, but I can't understand why, could you guys please look at it? http://img219.imageshack.us/my.php?image=utennavnwv7.jpg

Homework Statement Solve the integral using trigonometric substitution. \int\frac{\sqrt{4x^{2}+9}}{x^{4}}dx Homework Equations 2x=3tan\theta x=2/3 tan\theta dx=2/3 sec2\thetad\theta \sqrt{4x^{2}+9}=3sec\theta The Attempt at a Solution \frac{8}{9} \int...

I understood the concept and definition of marginal rate of substitution , and also MRS = -(dy/dx) , but why is dy/dx never positive ?

Homework Statement \int \frac{e^{3x}dx}{\sqrt{1-e^{2x}}} Homework Equations The Attempt at a Solution Alright so I am able to do other similar problems fine, I think it is the "e" that is throwing me off as well as the fact that the "x" is in the exponent. I started the...

My next project is to build a simple TEA nitrogen laser, as seen here: http://photonics.tfp.uni-karlsruhe.de/1/a-homemade-uv-laser.html Would it be acceptable to substitute two strontium titanate ceramic caps, each rated 50KVDC @ 910pf, in place of the suggested aluminum foil / plastic...

Homework Statement dy/dx = \frac{[2cos(x)^2-sin(x)^2+y^2]}{[2cos(x)]} Substitute y(x) = sin(x) + \frac{1}{u(x)} Homework Equations By doing the substitution, it will yield the differential equation for u(x) du/dx = -u tan(x) - \frac{1}{2}sec(x) The Attempt at a Solution I figured out i...

Wow I am so very bad at differential equations.. :( The problem Here is the exact problem I'm given: http://img229.imageshack.us/img229/9025/10640260bs5.jpg attempt at a solution I'm guessing that I need to differentiate y(x) that I am given and substitute that into the left hand side and...

Homework Statement \int{cos^4 6x sin^3 6x dx} Homework Equations The Attempt at a Solution I've gotten this far but now I'm stuck: \int{cos^4 6x sin 6x sin^2 6x dx} = \int{cos^4 6x}*(\frac{1-cos 12x}{2})sin 6x dx

Hi, We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution. We had a problem like this: \int cos^3 (x) dx Then we did: \int (1 - sin^2 (x)) cos(x) dx Starting u-substitution: u =...

The question is to convert the infinity limits of the integral \int^\infty_{-\infty} e^{{-x}^2} dx to finite limits \int^{u_a}_{u_b} g(u) du using the substitution u = tanh(x). How do I go about it?

Hey all, i think I'm doing most of this right, but I'm missing a coefficient somewhere when integrating or something... Homework Statement Substitute v=y/x into the following differential equation to show that it is homogeneous, and then solve the differential equation...

Homework Statement f(h+1)-f(h)/h. If f(x)=1/x, simplify. Homework Equations The Attempt at a Solution 1/x+1-(1/x)/h is the answer 1/h? I am not sure if i substituted this correctly or if I solved this right. I put 1/x in everywhere there was a f(h).

Substitute the letters by a different digit from 0 to 9 to satisfy this cryptarithmic long division problem. ....N K T ...------------------- F A R |...F R M N K B ...A K K N ...--------------------- ..... A B I K ...AM O K ...--------------- .....R T I B .....R A K T...

Homework Statement Use trigonometric substitution to evaluate \int{\frac{x^2}{\sqrt{9-x^2}}}dx The Attempt at a Solution Let x=3\sin\theta then dx=3\cos\theta d\theta \int{\frac{x^2}{\sqrt{9-x^2}}}dx =\int{\frac{9\sin^2\theta}{3\sqrt{1-\sin^2\theta}}}\ 3\cos\theta \ d\theta...

1. Homework Statement : using the substitution u=3x+4, work out: \int 2x \sqrt{3x+4}2. The attempt at a solution: \int 2x \sqrt{3x+4} u=3x+4 \rightarrow \mathrm{d}x = \frac{\mathrm{d}u}{3} \int \left( \frac{u-4}{3} \right)\left(u^{\frac12}\right) \ \frac{\mathrm{d}u}{3} \frac19 \int u^{\frac32}...

This is kind of an awkward post, but: The only topics that have always bugged me in calculus I-III are those which deal with differentials... I've convinced myself (and proven) that if a function can be written as f(x)dx = g(y)dy, then it is possible to "separate" the variables and solve the...

The question is: Use x = \tan \theta , \frac{-\pi}{2} < \theta < \frac{\pi}{2} to show that: \int_{0}^{1} \frac{x^3}{\sqrt{x^2+1}} dx =\int_{0}^{\frac{\pi}{4}} \tan^3 \theta \sec \theta d\theta Using that substitution, I got it down to: \int_{0}^{\frac{\pi}{4}} \frac{\tan^3...

Homework Statement If u=g(x) is a differentiable function whose range is an interval I and f is continuous on I, then Integral f(g(x)g'(x)dx=Integral f(u)du. Homework Equations The Attempt at a Solution

Homework Statement The d.e y' = (y+2x)/(y-2x) is NOT seperable, but if you use a substitution then you obtain a new d.e involving x and u, then the new d.e is seperable... Solve the original d.e by using this change of variable method Homework Equations I'm going to use the...

Homework Statement Use the transformation u = 3x + 2y and v = x + 4y to evaluate: The double integral of (3x^2 + 14xy + 8y^2) dx dy for the region R in the first quadrant bounded by the lines y = -(3/2)x + 1, y = -(3/2)x + 3, y = -(1/4)x, and y = (-1/4)x + 1. Homework Equations...

Given y' = y / (x + y^2), the substitution u = y^2 will give a homogeneous DE which can then be easily solved. Is there a substitution which would make things easier?

Problem: (tdt)/(4-t^4)^(1/2) Attempt: I want the derivate of whatever i make u equal to, to equal something outside of u therefore I will factorize the denominator to equal -(-2+t^2)(2+t^2) and make u equal to (2+t^2) so that du=2tdt Balance the equation so that one side is equal to the...

Homework Statement Using the substitution u² = 2x - 1, or otherwise, find the exact value of \int^{5}_{1} \frac{3x}{\sqrt{2x-1}}dx The Attempt at a Solution Right let's rearrange u in terms of x (i think that's how you say it): x = \frac{u^{2} - 1}{2}And now get an expression for dx u =...

Homework Statement \int2e^-^7^xdx Homework Equations None The Attempt at a Solution (\frac{-2}{7})(\frac{e^-^7^x}{-7})+C This is as far as I can go, but the answer is: \frac{-2e^-^7^x}{7}+C

Integrate the following: (x^3+x^2)/(1+x^4) I have been taught only integration by substitution. My teacher told me that this can be solved using that ith some trick. I have tried for a long time. All that I can do was to convert the numerator to x^2(x+1) and the denominator to...

Evaluate the following integral using integration by substitution: http://img254.imageshack.us/img254/750/44900023cm4.png [/URL] Here is my attempt: Let x = sinu, then dx/du = cosu Substituting gives, ∫1/(1-sin2u)×cosu du = ∫1/(1-sin2u)×cosu du = ∫cosu/√cos2u du = ∫cosu/cosu...

Homework Statement √(9-x²) / (x²) Homework Equations Just trig substitution The Attempt at a Solution Ok, for trig sub I did u=asinΘ x=3sinΘ 9-x²=9-9sin²=9(1-sin²Θ) so putting it into the equation √9cos²Θ=3cosΘ/x^2 where do I go from here, I tried getting help at Math...

Homework Statement I'm not sure how to proceed here. The first one asks me to find the area of a surface obtained by rotating the curve y = cos(x), 0 \leq x \leq\ \frac{\pi}{3} The second one asks to Solve: \frac{dy}{dt} = \frac{ty+3t}{t^2+1}\ y(2)=2 Homework Equations The Attempt at...

I'm looking to solve this integral with the tan(x/2) substitution but so far, I don't know what to do. Homework Statement \int\sqrt{1-sinx}dx Homework Equations u=tan(x/2) The Attempt at a Solution Well, using the tan(x/2) substitution, I get that: sinx=\frac{2u}{1+u^2}...

Homework Statement int sqrt 8x-x^2 Homework Equations trig sub The Attempt at a Solution complete the square integral becomes int sqrt 16-(x-4)^2 let x-4= 16sin(Q) sqrt 16-(x-4)^2 =sqrt 16-256sin^2(Q) dx= 16cos(Q)dQ =...

so I'm having problems with the coefficients in this problem. \int(10z+8/z^2-8z+41)dz i know that the main chunk is (a)ln|(z-4)^2+25|+(b)arctan((z-4)/5) a and b are 5 and 32/5 respectively the problem is i can't seem to split up the top so that the first portion is the derivitive...

Homework Statement Hey, it's me again. This method is giving me some trouble. This is the first problem: \int^3_0\ x^2\sqrt{9-x^2} \ dx The second problem is: \int\frac{dx}{\sqrt{2x^2+2x+5}}. How do I use a trig. substitution to start on this one? Homework Equations The Attempt at a...

[SOLVED] Integral with trig substitution Homework Statement Find \int(x^3)/\sqrt{x^2-9} Homework Equations Trig substitution. sin^2 + cos^2 =1, and other things that you can figure out from that. Half angle formula, cos^2\theta=(1+cos(2\theta) )*.5 The Attempt at a Solution...