3 years ago

What is the volume of the prism?

Mathematics

1 answer:

Sav [38]3 years ago

5 0

Answer:

if thers 480 its 480

Step-by-step explanation:

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$\displaystyle \pi \int_{\pi/2}^\pi (9\sin(x))^2\,\mathrm dx = 81\pi \int_{\pi/2}^\pi \sin^2(x)\,\mathrm dx$

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$\displaystyle 81\pi \int_{\pi/2}^\pi \sin^2(x)\,\mathrm dx = \frac{81\pi}2 \int_{\pi/2}^\pi (1-\cos(2x))\,\mathrm dx \\\\ =\frac{81\pi}2 \left(x-\frac{\sin(2x)}2\right)\bigg|_{\pi/2}^\pi \\\\ = \frac{81\pi}2 \left( \left(\pi-\frac{\sin(2\pi)}2\right) - \left(\frac\pi2 - \frac{\sin(\pi)}2\right) \right) \\\\ = \boxed{\frac{81\pi^2}4}$

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First, what graph is it? It is a rational function.
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