Compute the volume of another solide

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Homework Statement



Compute the volume of the solid bounded by the surface z = sin(y), the planes x = 1, x = 0, y = 0, and y = pi/2, and the xy plane.

Homework Equations



None.

The Attempt at a Solution



Double Integral sin(y) dA

where the limits of integration is:

0 </ x </ 1

0 </ y </ pi/2

After calculating the double integral, I got 1. Can anyone verify my work?
 
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number0 said:
After calculating the double integral, I got 1. Can anyone verify my work?

I get V = 1 as well.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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