What is Integrate: Definition and 650 Discussions

Homework Statement Evaluate $$\int_ \ \sqrt[2]{9-x^{2}} \, \mathrm{d} x.$$ Homework Equations U substitution Integration by parts The Attempt at a Solution My teacher said it wasn't possible "by hand", but Wolframalpha provided a step-by-step solution. I'm clueless as to how wolfram came...

Homework Statement Integrate ettdt using integration by parts.2. The attempt at a solution Seems like a very easy problem; however, I just started learning integration by parts-- didn't understand this. So the book's method: u=t...

Homework Statement Integrate \sqrt{x-x^2} The attempt I did a trig substitution, letting cos(\theta)=\frac{x}{sqrt(x)} and after some manipulation ended up with -2\int \ |sin(\theta)cos(\theta)|sin(\theta)cos(\theta) d\theta which I have no idea how to integrate. If I make a...

I have the following equation \frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0 where y is a function of x and m is a function of y. If I integrate this equation first with respect to y should I get a function of x as the constant of integration (say C\left(x\right)) or it is just...

Homework Statement ∫[(1+tanx.tan(x+a)]dx Homework Equations The Attempt at a Solution ∫sec^x.tan(x+a) after that i don't know as i tried method of substitution by putting x+a=t but i am not getting the answer as its form on the whole remains same

Homework Statement integrate dx / (x^2 - 1)^2 Homework Equations The Attempt at a Solution There is nothing i can substitute to get rid of x. Except x=sqr(t), but then dx is 1/2sqr(t) so i get: ∫( dt / (t-1)^2 * 2sqr(t) ) and it's still impossible to integrate.

Homework Statement http://i50.tinypic.com/zxw6qr.png a>0 a ∫ x√(x^2+a^2)dx (a>0) 02. The attempt at a solution u=x^2+a^2 du=2xdx I looked it up online and I saw you needed to use trig. How do you use trig for this problem? Note: I have not learned integration by parts, just u-sub.

In a continuous isotropic medium having refractive index n, (not constant) the ray path can be described by the following equation d/ds(n dr/ds)) = grad (n) with an obvious meaning of the symbols (for they who can help me!). I wrote a code to calculate the ray path. I found result...

Homework Statement I'm having some troubles with my calculus. I can't get from the first step to the second step in the example below: Homework Equations http://img853.imageshack.us/img853/4350/unavngivetpn.png The Attempt at a Solution \int_{-L/2}^{L/2} [R^2 + (Z-Z_0)^2]^{1/2} -...

Homework Statement The reduction formula is: \int (1-x^2)^n dx = (1-x^2)^n x + 2n \int x^2(1-x^2)^{n-1} dx and the question is: use this formula above how many times is necessary to prove: \int^{1}_{0} (1-x^2)^n dx = 2n \frac{2(n-1)}{3} \frac{2(n-2)}{5} ... \frac{4}{2n-3}...

∫Homework Statement "Express the integrand (what does "integrand" mean?) as a sum of partial fractions and evaluate the integrals. ∫(x + 4)/ (x^2+5x-6) dx Homework Equations The Attempt at a Solution x^2+5x-6 = (x-1)(x+6) Gives: ∫ A/(x-1) + B/(x+6) dx Findig A and B: A(x+6) + B(x-1)...

Homework Statement Compute ∫f ds for f(x,y)= √(1+9xy), y=x^3 for 0≤x≤1 Homework Equations ∫f ds= ∫f(c(t))||c'(t)|| ||c'(t)|| is the magnitude of ∇c'(t) The Attempt at a Solution So, with this equation y=x^3 ... I got the that c(t)= <t,t^3> c'(t)=<1,3t^2> I know that from the equation...

Homework Statement \frac{dy}{dx}+\frac{y}{(1+x^2)} = \frac{\arctan x}{(1+x^2)} when y(\frac{\pi}{4})=0 Homework Equations \frac{dy}{dx}+Q(x)*y=F(x) The Attempt at a Solution y=u*v u*\frac{dv}{dx}+v*(\frac{du}{dx}+\frac{u}{(1+x^2)})=\frac{\arctan x}{(1+x^2)} \frac{du}{dx}+\frac{u}{(1+x^2)}=0...

I have a grid and on each point on the grid I have discrete velocity data. I however don't have anyalytical function. I need to integrate the points and check where in space they will be after some time. I know it very easy to do it with runge-kutta if i have the analytical function for velocity...

V = \int \frac{x}{(sin(x^2))^2}.dx I tried to solve this by parts or by substitution but that doesn't seem to work. Any Idea how to solve it :/

→Homework Statement Integrate the improper integral (use correct notation). State whether it's converging or diverging. 10 ∫ 7/(x-9)^2 dx 8 Homework Equations b c ∫ f(x) dx= lim ∫ f(x) dx a c → d a The Attempt at a Solution...

How do you integrate quotients? Let's practice with one like... \int\frac{3x + x^{2}}{5x - 1} dx Thanks for the help!

How do i integrate this ? ∫ (x/(x+2)) .dx Any idea ?

Homework Statement I am in the process of solving second order differential equation by the variation of parameters method. I need to calculate ∫(et)*(tant)2 dt Homework Equations (tanx)2 = (secx)2-1 ∫(secx)dx= lnlsecx*tanxl The Attempt at a Solution I have used the trig identity to get...

Homework Statement ∫Bdot[∇×A]dV=∫Adot[∇×B]dV Prove this by integration by parts. A(r) and B(r) vanish at infinity. Homework Equations I'm getting stuck while trying to integrate by parts - I end up with partial derivatives and dV, which is dxdydz? The Attempt at a Solution I...

Homework Statement Integrate cos(x)-cos(x-c) from 0 to c/2 Homework Equations sin(x-c)=sinxcosc-cosxsinc The Attempt at a Solution sin(x)-sin(x-c) from 0 to c/2 =sin(c/2)-sin(c/2)cos(c)+cos(c/2)sin(c)-sin(0)+sin(-c) =sin(c/2)-sin(c/2)cos(c)+cos(c/2)sin(c)-0-sin(c) Correct...

Homework Statement Integrate from zero to infinity; f(x)=\sqrt(x)log(x)/(x^2+1) Homework Equations Branch cut makes log(z)= ln|z|+i Arg(z) Poles are at +/- i and Res(z=i) is \pi/4 e^(i \pi/4) I'll need to close the contour; probably as an annullus in the top half of the...

Please intergrate: (x+3)/(x^2+4x) is it even possible to integrate this? The question in the book was (x+2)/(x^2+4x) and it can nicely be integrated to 0.5ln(x^2+4x), but by changing the 2 to a 3 f'(x) don't go into each other. if you know what i mean.

The problem shows a picture of a surface of a half sphere. It is labeled surface 1 being the disk of the top of the half sphere. Surface 2 is the remaining surface of the half sphere. R is the radius. The magnetic field is uniform and makes an angle theta with the vertical (or with the...

One last question to Integrate x^2/(1+4•x^2). I would assume you would do long division but 4x^2 is bigger than x^2. so would you either pull out a 1/4 and it would be 1/4 ∫ x^2/(1/4+•x^2) dx or would the first term when doing long division be 1/4? or am I just totally wrong and you...

T(z,t) = ∫ ( exp(-αz)* erfc(-α*sqrt((k*t)/(c*ρ))+0.5 sqrt((c*ρ*z)/(k*t)))*exp( -((t-ζ)/ζ0)^2) integrate with respect to ζ in the limits 0 and t Help will be greatly appreciated

Homework Statement ∫√(((x)^2)/2 + 9) dxHomework Equations --- The Attempt at a Solution I'm having a horrible time trying to do it. Problem is, I don't know how to start. The only thing I can think of is using trigonometric substitution. But I don't know how to manipulate the function in...

Hi, so I have a question where it asks me to find the distance between t = 0 and t = 60 for the equation v = 1/6(t(60 - t)). First I had to find the values of t which the object moving was stationary, that was simple enough. (It's been around a month and a half since I did rectilinear motion)...

Homework Statement See uploaded file Homework Equations See Uploaded file The Attempt at a Solution Ok problem 1 I have with the solution why is (KT/HC)^4 on the outside of the integral and why is it to the 4th power. I assume it is to find (lamda)^5 but I would think if that was the...

Homework Statement Suppose I have d/dx f(x) = 0, and I integrate both sides with respect to x. I have worked out two possibilities, and I am not sure which is correct: 1) ∫ d/dx f(x) dx = 0 → ∫ f'(x) dx = 0 → f(x) + C = 0 or 2) ∫ d/dx f(x) dx = 0 → d/dx ∫ f(x) dx = 0...

Hello, I'm doing a quantum mechanics problem from Griffiths chapter 1 where I'm trying to find the expectation value of x^2 given the function ρ(x) = Aexp[-λ(x-μ)^2]. The problem is in the title, but I'll rewrite it here simplified: ∫(x^2)exp(-x^2)dx Subbing u = x^2 <=> x = sqrt(u) => dx...

Homework Statement The Attempt at a Solution It looks like they think the integration of (cos(p)/(sqrt(1-sin^2p)))dp = 1. I don't see how. I looked at my table of common integrals and I didn't see it. I know that cos^2 + sin^2 = 1 of course but I don't how that helps with the above.

Homework Statement If F(x)=∫from 0 to g(x) of 1/(√(1+t^3)) dt and g(x)= ∫from 0 to cos(x) of 1+sin(t^2) dt, then find f'(pi/2) Homework Equations The Attempt at a Solution Tried FTC parts 1 and 2

Given x=rcosθ, y=2rcosθ Integrate the following: I = ∫∫D{x2+y2/4} dxdy D = {(x,y)|x2+y2/4≤1} My first attempt was that I substitute the polar coordinate given into the domain for x and y and so I got rcosθ+rsinθ≤1. And from here, I don't know what else to do,I am stuck.Help.

Homework Statement ∫\frac{sin\Theta}{1+sin^2\Theta} d\Theta on [0,\frac{\pi}{2}] Homework Equations I substituted: u=cos\Theta du=-sin\Theta The Attempt at a Solution = ∫ \frac{sin\Theta}{1+1-cos^2\Theta} = ∫ \frac{sin\Theta}{2-cos\Theta} = ∫ \frac{sin\Theta}{2-u^2} =...

Homework Statement ∫ex3 dx ? The Attempt at a Solution no idea

Hi, I was wondering if there's a simpler way to integrate this? I got the answer by expanding one by one but that's such a long process! I got the answer 104/5 which is correct,though. ∫∫∫D (x + y + z)^4 dxdydz D = {(x,y,z) | -1≤ x ≤1, -1≤y≤1, -1≤z≤ }

Hi, I was wondering if there's a simpler way to integrate this? I got the answer by expanding one by one but that's such a long process! I got the answer 104/5 which is correct,though. ∫∫∫D (x + y + z)^4 dxdydz D = {(x,y,z) | -1≤ x ≤1, -1≤y≤1, -1≤z≤ }

Homework Statement As stated in the title. Homework Equations No equations The Attempt at a Solution Honestly, I'm stuck. I have no idea where to go. My only thought is to multiply the top and bottom by sinx but where would that get me?

Is it possible to integrate x^2*e^(x^2)? Also, is it possible to integrate x*e^(x^2)? If so, would you do it by parts?

As time goes by in my physics career I find myself less and less motivated to do integrals by hand and more relying on integral tables to quickly look up the answer. I just find doing integration out by hand tedious, especially ones that require multiple integrations by parts or involve trig...

Homework Statement In the section of the book of integration by parts, there is an exercise that I don't even know how to tackle anymore. It's this: \int \frac{xe^{2x}}{(1+2x)^2} dx Homework Equations {uv} - {\int v{du}} The Attempt at a Solution u = x ; du = 1...

Hi all, I've written a simulation of water flow in two dimensions in F90 but I'm having some trouble with it. Water flows from one cell to another using an equation for rate of change of depth and an algorithm for assigning flow direction. The flow direction bit is fine but the dD/dt...

Homework Statement Integrate (x-x^2)^1/2 from 1/2 to 1. I tried to use substitution with x=sinu, dx=cos du to get: sinu(1-sinu)^1/2 cosu du but no idea where to go from there! Also tried integration by parts, but it didn't work! Help!

Hi, simple question, but difficult to find an answer for me How to integrate sqrt((ax+b)/x) dx ? a,b constants and x variable if it matters, I would be happy if you could solve it just for both a,b >0 Thanks

Homework Statement \int^{2\pi}_0{cos(x)cos(nx)dx}=?,n\in Z Homework Equations The Attempt at a Solution I think that this eq has zero solve. However my teacher says that its incorrect. cos(x) cos(nx) = 1/2 (cos (x-nx) + cos (x+nx))...

So a question for a test I just had was integrate by substitution: Sin(x)e^Cos(x). I did something like this: Let u=Cos(x) du=-sin(x) dx ∫sin(x)e^Cos(x) dx = ∫-e^u du =∫-e^Cos(x) du...

EDIT: I solved it. Sorry for waste of time! :( Here is the function ψ[x]: 0.0000551056 a0.25 (30240. a0.5 x - 80640. a1.5 x3 + 48384. a2.5 x5 - 9216. a3.5 x7 + 512. a4.5 x9)(-((a x2)/2)) I am trying to integrate ψ[x]*ψ[x] over all space (-infinity to +infinity). I don't get any error...

Homework Statement Question #4Homework Equations The formula for step 1 is supposed to be general equation for moment of inertia.The Attempt at a Solution as seen. The answer to the question is 5.870 My attempt: 1/3pi^3 * -cos(pi) still wrong.

Homework Statement Hi. My first post! I'm trying to solve for where a is a constant: ∫ (x/a)1/2*(x/(x-a)) dx Homework Equations See above The Attempt at a Solution I've tried integration by parts by setting u=(x/a)1/2 but I end up having to solve ∫ (x/a)1/2ln(x-a) - which I...