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Popular >

integral from-2 to 2 of integral from 0 to sqrt(4-x^2 of)sqrt(x^2+y^2)

Solution

\int_{- 2}^{2} \int_{0}^{4 - x^{2}} x^{2} + y^{2} d y d x

Solution

\frac{8 π}{3}

+1

Decimal Notation

8.37758 \dots

Solution steps

\int_{- 2}^{2} \int_{0}^{4 - x^{2}} x^{2} + y^{2} d y d x

Convert to polar coordinates

= \int_{0}^{π} \int_{0}^{2} r^{2} r d r d θ

\int_{0}^{2} r^{2} r d r = \frac{8}{3}

= \int_{0}^{π} (\frac{8}{3}) d θ

\int_{0}^{π} (\frac{8}{3}) d θ = \frac{8 π}{3}

= \frac{8 π}{3}

Popular Examples

integral from 0 to pi of integral from 0 to pi/2 of cos(x+2y)

\int_{0}^{π} \int_{0}^{\frac{π}{2}} cos (x + 2 y) d y d x

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\int \int ln (x) d x d x

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\int \int e^{2 x} d x d x

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\int \int \int x^{2} d x d x d x

Frequently Asked Questions (FAQ)

What is the integral from-2 to 2 of integral from 0 to sqrt(4-x^2 of)sqrt(x^2+y^2) ?
The integral from-2 to 2 of integral from 0 to sqrt(4-x^2 of)sqrt(x^2+y^2) is (8pi)/3