## Task Condition

Calculate the volumes of solids formed by rotating figures bounded by the graphs of functions. The axis of rotation is $O y$.

$$
y=\arcsin x, y=\arccos x, y=0
$$
## Solution

![](https://cdn.mathpix.com/cropped/2024_05_22_cfec74fe4e2360126fc5g-53.jpg?height=1114&width=1394&top_left_y=965&top_left_x=114)

$$
V_{y}=\pi \int_{0}^{\frac{\pi}{4}}\left(\cos ^{2} y-\sin ^{2} y\right) d y=\frac{1}{2} \pi \int_{0}^{\frac{\pi}{4}} \cos 2 y d(2 y)=\left.\frac{1}{2} \pi \sin 2 y\right|_{0} ^{\frac{\pi}{4}}=\frac{\pi}{2}
$$

Source — "http://pluspi.org/wiki/index.php/%D0%9A%D1%83%D0%B7%D0%BD%D0%B5%D1%86%D0%BE%D0%B2_%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D1%8B_%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_21-27" Categories: Kuznetsov Problem Book Integrals Problem 21 | Integrals

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Created by GeeTeatoo

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## Problem Kuznetsov Integrals $21-28$

## Material from Plusi