Integrate Definition and 642 Threads

Homework Statement If a car is going 30m/s and see's an accident 60 meters in front of him/her, at what deceleration must the car apply brakes in order to stop in time?Homework Equations s(t) = \int(v)t v(t) = \int(a)tThe Attempt at a Solution So I know the physics equation that I could use for...

how do you integrate 1/(x2 + 1)2 ? i have tried integration by partial fractions but when you set 1 equal to (Ax +B)(x2+1) + (Cx + D) this leads to A=B=C=0 and D=1 which just gives you the original equation

I am working on a problem (not homework) on diffusion and have landed up with an integral which I simply cannot integrate. No method seems to work. I shall first describe the problem a little for you to check if I have landed up on the correct route, and then present the integral. According to...

Homework Statement What is integral of e^t (1+3sint)? I tried integ by parts but its not working Im familiar with the technique where you end up with two idental integrals on either side, then you add one side to the other, and divide by 2. This isn't working though. Mainly because the RHS...

Homework Statement Use trial wavefunction exp(-bx^2) to get an upper limit for the groundstate energy of the 1-d harmonic oscillator The Attempt at a Solution This is always going to give an integral of x^2*exp(-x^2). How do you do it? :/

I think I've done it at least once every day for the past week. I week getting it wrong on the homework site. Worst off all, it only alows 5 entries. I've used 4. Please help.

Integrate int(0topi)int(0tosinx)ydydx

How do I integrate this? 1/(x^2-1)^.5 How do I integrate this? x/(x^2-1)^.5 And this 1/(x^2-1)^.5

Homework Statement Use separation of variables to solve (x+2y)y'=1 y(0)=2Homework Equations u=2y+x >>I did not know how to start this, so i looked at the back of the book and it said to use that substitution y=(u-x)/2, du=2dy+dx, dy=(du-dx)/2 The Attempt at a Solution so i got the following...

Homework Statement How do we evaluate integrals of COMPLEX-valued functions (like the following)? 2 ∫ exp[-(2+3i)x] dx 0 This integral is appearing in my PDE course in the topic of Fourier transform, but I have no background of how to integrate complex-valued functions. Looking...

Homework Statement integrate: 4*cos(n pi t) d(t) Homework Equations The Attempt at a Solution is it: [4sin(n pi t)]/n.pi or [4t sin (n pi t)]/n.pi any help very much welcome.

What does the following mean - \int \textbf{F} \cdot d \textbf{r} I know that its equal to work done. but i have problem in understanding it, what's the varibale. i am familiar with integrate cosxdx. what's is similar to dx in above equation. is it ds. Now how can one get to this from above...

Dear all, I would like to evaluate \int\frac{1}{1-2sin\left(x\right)}dx Firstly, I make use of the Weierstrass substitution method by letting: u=tan\left(\frac{x}{2}\right) and therefore sin\left(x\right)=\frac{2u}{1+u^{2}} and dx=\frac{2}{1+u^{2}}du Eventually I can...

Homework Statement I'm a little confused with this integral: \int^\infty_{-\infty}e^{-a|x|}\,dx Homework Equations The Attempt at a Solution Now, I believe the typical way to evaluate this is to say, hey, because of the |x|, this thing is symmetric about the x axis, and so we can...

Homework Statement \frac{dz}{d\theta} = \int\sqrt{a^{2} + z'^{2}} I think I would have to make a substitution but I'm not sure which one to make...

Homework Statement I am losing my first year calculus skills :( I don't remember how to integrate x5 exp(x2). What is the fastest way? Homework Equations N/A The Attempt at a Solution Maybe we need to integrate by parts? But how should I set u and dv? Thanks for any help!

Hi there, I am having a hard time figuring out how to integrate cos(2x)^N where N=0,1,2... Can anyone give me and hints/tips on how to go about integrating this? Thanks!

Homework Statement Define the function over the four intervals in order to find the area under the curve from [-4,6]. To do so, find the equations of the line and circle, using the data in the graph. Homework Equations None? The Attempt at a Solution To be honest, there...

Homework Statement In a sphere of radius R, the charge density varies as \rho(r) = BrN. There is no charge outside the sphere. B and N are constants. a.) Find the charge enclosed in a sphere of radius r<R.Homework Equations \rho=dq/dvThe Attempt at a Solution I integrated \rho(r)(4\pir2dr)...

Hi, the question is integrate x^2 /square root (x^2 +1). I tried to do it but i was stucked in the very last step.at the end,I got x/2 * cosh(arcsinh x) + 1/2 * arcsinh x - arcsin (square root (x^2 + 1)) +C. I dunnoe how can I simplify cosh(arcsinh x) into simplier form in term of x. I hope...

Homework Statement \int (3x-5)e^{4ln(x)} Homework Equations The Attempt at a Solution Any ideas?

How can you intgertate the 1/cos(x)? The right answer can be found in Wolfram alpha at http://www.wolframalpha.com/input/?i=1%2Fcos(x) My first wrong answer was ln(cos(x)). It suggests me that you cannot use the rule, ln(x), for trigonometric functions

1.a Evaluate the following. Show all work. http://img90.imageshack.us/img90/289/problemu.png 1.b Differentiate. http://img293.imageshack.us/img293/1440/problem2.png Homework Equations ƒ b-a f(x)-g(x) The Attempt at a Solution...

can some one explain to me how the set of all solutions for dy/dx = 3y is. y= Ce^3x

Homework Statement Find \int{tan^2xsec^2xdx} Homework Equations tan^2x=sec^2x-1 (1) The Attempt at a Solution Using (1): \int{(sec^4x-sec^2x)dx} Now, \int{sec^4xdx}-\int{sec^2xdx}=\int{sec^4xdx}-tanx+c I can't figure out how to solve \int{sec^4xdx} though.

Homework Statement The whole expression is \frac{(-1)^n (2n)!}{2^{2n} (n!)^2} \int^{1}_{-1} (x^2-1)^n dx and the answer should be \frac{2}{2n+1} but I don't know how to get there. I came across this while checking the orthogonality of the associated Legendre functions. Homework...

Dear all, i met a problem that i couldn't get the on axis field of a finite solenoid that integrating from a thin shell solenoid equation. The thin shell equation link: http://www.netdenizen.com/emagnet/solenoids/thinsolenoid.htm And the on axis finite solenoid equation link...

Integrate the following---> {x3+1/(whole root over)x2+x}dx

Hi everyone, Can you tell me how to integrate the following equation? \int\frac{1}{x^2 + 1} \ dx I've tried the substitution method, u = x^2 + 1, du/dx = 2x. But the x variable is still exist. Also, the trigonometry substitution method, but the denominator is not in \sqrt{x^2 + 1}...

Homework Statement \frac{dx}{(4+x^2)^2}Homework Equations I understand that \frac{dx}{a^2+u^2} = \frac{1}{a} tan -1 \frac{u}{a} + cThe Attempt at a Solution The extra square is throwing me off for some reason. If I let a=2 and u=x it doesn't seem to help because of the whole term being...

Homework Statement Integrate x^5sin(x^3). Using Integration by parts. The Attempt at a Solution I don't know which one to take du and u can anyone please help me out? Thanks a lot before hand!

f(x)=40*e^(-0.5x)

Homework Statement Integrate Sqrt[ ex+1] 2. The attempt at a solution I first multiplied the equation by e^x / e^x, then tried substitution, with u = e^x + 1 du = e^x dx This gave me: Integral 1/(u-1) * (u)^1/2 du However, I'm stumped at this part. Substitution here doesn't...

Homework Statement integrate: e(x^2 +x)(2x+1) dx The Attempt at a Solution let u= e(x^2 +x) du=e(x^2 +x)(2x+1)dx integral e(x^2 +x)(2x+1) dx = integral 1/u du am I on the right track? i didnt get the same answer as the prof...

Homework Statement I am having trouble solving the following: \intsin(lnx) dx The Attempt at a Solution I let u = ln x but this makes xdu = dx so I am left with \intx sinu du

Homework Statement Integrate (a^x + b^x)^3 /((a^x)*(b^x)) The Attempt at a Solution I have only 2 semesters of calculus under my belt yet nothing in my experience has taught me to do anything like this

Homework Statement I have to solve the following integral 1/(sqrt[x] * ln[x]) from 2 to infinity Homework Equations The Attempt at a Solution u= ln[x] dv=1/sqrt(x) du= 1/x v= 2 sqrt(x) If I do this I get lim (ln b/ sqrt[x] - 4 sqrt[x] -...

Homework Statement The problem states: Use substitution to solve: y'=1/(x+y)^2-1Homework Equations The Attempt at a Solution I used the substitution of v=x+y resulting in the answer y=[3(x-C)]^(1/3) - x but I'm not too sure that's right Can some help with the answer and the steps for...

Homework Statement Compute the Fourier cosine series for given function: f(x)=sinx 0<x<piHomework Equations for cosine series of f(x) on [0,T]... use this general equation: http://mathworld.wolfram.com/FourierCosineSeries.html The Attempt at a Solution so I get: a0 = (2/pi) *...

Hi! I'm having trouble understanding my textbook, so can someone please explain to me how they got from \int1/(1+x)2 dx, with the range of the integral from 0 to x/n to 1 - n/(x+n) THank you So MuCh

Homework Statement When I plug in Integrate[ x/(1 + x), x] into Mathematica, I get x - Log[1 + x] which I've been able to recreate on paper. However, when I plug in Integrate[ 2 x/(1 + 2 x), x] I get 1/2 + x - 1/2 Log[1 + 2 x] but on paper I get x - 1/2 Log[1 + 2...

Homework Statement convert double integral from line one to polar integral and then evaluate see problem 12 attachment Homework Equations y=rsinx x=rcosx r^2=x^2+y^2 The Attempt at a Solution see problem 12 attachment I calculate a area of zero. are my limits wrong and if...

Homework Statement 4\int 1/ ( x^3 *( 1 - x^2)) dx Homework Equations Maybe integration by parts? The Attempt at a Solution This is actually a small fragment of a very large, long problem but, I cannot for the life of me think how to integrate this with there being a product...

Homework Statement \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x The Attempt at a Solution If I use u = \pi-x I get : \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x = \int_{0}^{\pi} \sin ( \cos x ) \mbox{d}x but then what?

How do you integrate (ln ln x)^n for any n?

~~ Integrate 3cos^2(x) Hey guys, Can you please show me a step by step integration for Find the solution for the differential equation : 3Cos2(x) , y= Pi , x = Pi/2 Thank you !

How does one integrate \int_0^\infty e^{-\beta x^2}\cos{(bx)} dx for positive beta and real b ? I was thinking maybe differentiation under the integral sign would do the trick, but I can't get anywhere.

how do i integrate this?? how do i integrate this function? \intdx/(ex-1)0.5 i have tried all the methods i know and haven't cracked it, the best try i have had so far is \intdx/(ex-1)0.5 ===>t=ex; dt=exdx \intdt/t*(\sqrt{t-1}) now from here i tried integration in parts and...

\int e^\sqrt[3]{x} dx Integration by parts, perhaps? But if that's the case, I have no idea which is right value for u and which is the right one for dv... Taking ln on both sides? Uh...hmm...I don't think that's how you work this question out... Any ideas, guys? :| Thanks!

how do i integrate this "e^[−(x/xa)]