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Q. 52

Expert-verifiedFound in: Page 1056

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 ${\int}_{-3}^{3}{\int}_{-3}^{3}{\int}_{-\sqrt{9-{x}^{2}}}^{\sqrt{9-{x}^{2}}}f(x,y,z)dydxdz.$

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

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 ${\int}_{-3}^{3}{\int}_{-3}^{3}{\int}_{-\sqrt{9-{x}^{2}}}^{\sqrt{9-{x}^{2}}}f(x,y,z)dydxdz.$

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