## Integral Volume

Limits, differentiation, related rates, integration, trig integrals, etc.

### Integral Volume

I have another question: simply, how would approach this question: Integral of [e ^ (x/pi) * sin x] ^ 2, where it is bounded by that same function, [0, pi], and the x-axis where the solid is revolved about the x-axis. Thanks. The integral above is part of the definite integral for a volume so the original equation is y = e ^ (x/pi) * sin x and I have already squared it and put the pi "outside" of the integral.
paulh428

Posts: 7
Joined: Wed Apr 27, 2011 11:17 pm

### Re: Integral Volume

paulh428 wrote:I have another question: simply, how would approach this question: Integral of [e ^ (x/pi) * sin x] ^ 2, where it is bounded by that same function, [0, pi], and the x-axis where the solid is revolved about the x-axis. Thanks. The integral above is part of the definite integral for a volume so the original equation is y = e ^ (x/pi) * sin x and I have already squared it and put the pi "outside" of the integral.

it this

$\int\limits_{0}^{\pi}\left[e^{x/\pi}\sin(x)\right]^2dx$

what you are trying to compute?

Martingale

Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA

### Re: Integral Volume

Martingale wrote:
paulh428 wrote:I have another question: simply, how would approach this question: Integral of [e ^ (x/pi) * sin x] ^ 2, where it is bounded by that same function, [0, pi], and the x-axis where the solid is revolved about the x-axis. Thanks. The integral above is part of the definite integral for a volume so the original equation is y = e ^ (x/pi) * sin x and I have already squared it and put the pi "outside" of the integral.

it this

$\int\limits_{0}^{\pi}\left[e^{x/\pi}\sin(x)\right]^2dx$

what you are trying to compute?

Yes. I'm just trying to compute that integral. I'm not worried about finding the limits of integration for now. Just the integration. Thanks so much for helping out on my problems, Martingale.
paulh428

Posts: 7
Joined: Wed Apr 27, 2011 11:17 pm

### Re: Integral Volume

paulh428 wrote:
Martingale wrote:
paulh428 wrote:I have another question: simply, how would approach this question: Integral of [e ^ (x/pi) * sin x] ^ 2, where it is bounded by that same function, [0, pi], and the x-axis where the solid is revolved about the x-axis. Thanks. The integral above is part of the definite integral for a volume so the original equation is y = e ^ (x/pi) * sin x and I have already squared it and put the pi "outside" of the integral.

it this

$\int\limits_{0}^{\pi}\left[e^{x/\pi}\sin(x)\right]^2dx$

what you are trying to compute?

Yes. I'm just trying to compute that integral. I'm not worried about finding the limits of integration for now. Just the integration. Thanks so much for helping out on my problems, Martingale.

$\left[e^{x/\pi}\sin(x)\right]^2=e^{2x/\pi}\sin^2(x)=e^{2x/\pi}\frac{1}{2}(1-\cos(2x))$

distribute and use integration by parts

Martingale

Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA