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number 42 please!

41-43 Evaluate the integral by changing to spherical coordinates.

1-x2 cV2-x2-

41. Jo

xy dz dy dx

42.

x2z + y2z + z3) dz dx dy

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07:17

$39-41$ Evaluate the integral by changing to spherical coordinates.$\int_{0}^{1} \int_{0}^{\sqrt{1-x^{3}}} \int_{\sqrt{x^{2}+y^{2}}}^{\sqrt{2-x^{2}-y^{2}}} x y d z d y d x$

07:03

$39-41$ Evaluate the integral by changing to spherical coordinates.$\int_{-2}^{2} \int_{-\sqrt{4-x^{2}}}^{\sqrt{4-x^{2}}} \int_{2-\sqrt{4-x^{2}-y^{\prime}}}^{2+\sqrt{4-x^{1}-y^{2}}}\left(x^{2}+y^{2}+z^{2}\right)^{9 / 2} d z d y d x$

08:56

$37-39$ Evaluate the integral by changing to spherical coordinates.$$\int_{0}^{1} \int_{0}^{\sqrt{1-x^{2}}} \int_{\sqrt{x^{2}+y^{2}}}^{\sqrt{2-x^{2}-y^{2}}} x y d z d y d x$$

06:05

$37-39$ Evaluate the integral by changing to spherical coordinates.$$\int_{-2}^{2} \int_{-\sqrt{4-x^{2}}}^{\sqrt{4-x^{2}}} \int_{2-\sqrt{4-x^{2}-y^{2}}}^{2+\sqrt{4-x^{2}-y^{2}}}\left(x^{2}+y^{2}+z^{2}\right)^{3 / 2} d z d y d x$$

04:04

Evaluate the integral by changing to spherical coordinates. 16 32 – x2 _ y2 J ^ xy dz dy dx x2 + y2

Transcript

Hi, in the given problem we have a definite integral from minus a to a and then from square root of a square minus y square minus to plus a square root of a square minus y square. Then the third integral is square root of a square minus x square plus y square, which is minus and then square root of a square minus x square plus y square and the integrand is x square z plus y square z plus z cube then dz dx dy. So, in the spherical coordinate let us say this is the integral I and the spherical coordinate this is written as integral from 0 to 2 pi and…

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