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Q. 52

Expert-verified
Found in: Page 1056

### Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

# In Exercises 45–52, rewrite the indicated integral with the specified order of integration.Exercise 42 with the order dy dx dz.

The given indicated integral with the specified order of integration is ${\int }_{-3}^{3}{\int }_{-3}^{3}{\int }_{-\sqrt{9-{x}^{2}}}^{\sqrt{9-{x}^{2}}}f\left(x,y,z\right)dydxdz.$

See the step by step solution

## Step 1. Given Information.

The given triple integral is ${\int }_{-3}^{3}{\int }_{-\sqrt{9-{x}^{2}}}^{\sqrt{9-{x}^{2}}}{\int }_{-3}^{3}f\left(x,y,z\right)dzdydx.$

## Step 2. Rewrite the integral.

We have to write the given integral in order of dy dx dz.

So, the limit of the integration will vary as follows:

The limit of y alters from $-\sqrt{9-{x}^{2}}\text{to}\sqrt{9-{x}^{2}}\text{.}$

The limit of x alters from $-3\text{to}3.$

The limit of z alters from $-3\text{to}3.$

Hence the indicated integral with the specified order of integration is ${\int }_{-3}^{3}{\int }_{-3}^{3}{\int }_{-\sqrt{9-{x}^{2}}}^{\sqrt{9-{x}^{2}}}f\left(x,y,z\right)dydxdz.$