What is the integral from-x to x of sqrt(x+y) ?

The integral from-x to x of sqrt(x+y) is (4sqrt(2)x^{3/2})/3

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integral from-x to x of sqrt(x+y)

\int_{- x}^{x} x + y d y

\frac{4 2 x ^{\frac{3}{2}}}{3}

Solution steps

\int_{- x}^{x} x + y d y

Apply u-substitution

: \int_{0}^{2 x} u d u

= \int_{0}^{2 x} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2 x}

= [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{2 x}

Compute the boundaries:

\frac{4 2}{3} x^{\frac{3}{2}}

= \frac{4 2}{3} x^{\frac{3}{2}}

Simplify

= \frac{4 2 x ^{\frac{3}{2}}}{3}

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