Question

Rewrite the following integral using the indicated order of integration and then evaluate the resulting integral. 1 14-x14 - x? SI S dy dz dx to dz dy dx 0 0 0 1 14-y14 - x2 ss S dy dz dx = SSS dz dy dx = 0 0 0 (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Answer 1

$\int _0^1\int _0^{\sqrt{4-x^2}}\int _0^{\sqrt{4-x^2}}1dzdydx$\

$\int _0^{\sqrt{4-x^2}}1dz=\sqrt{-x^2+4}$

$=\int _0^1\int _0^{\sqrt{4-x^2}}\sqrt{-x^2+4}dydx$

$_0^{\sqrt{4-x^2}}\sqrt{-x^2+4}dy=-x^2+4$

$=\int _0^1\left(-x^2+4\right)dx$

$\int _0^1\left(-x^2+4\right)dx=\frac{11}{3}$

$=\frac{11}{3}$

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