## Integral Volume

Limits, differentiation, related rates, integration, trig integrals, etc.
paulh428
Posts: 7
Joined: Wed Apr 27, 2011 11:17 pm
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### 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.

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
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### Re: 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.
it this

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

what you are trying to compute?

paulh428
Posts: 7
Joined: Wed Apr 27, 2011 11:17 pm
Contact:

### Re: 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.
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.

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: 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.
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