What is the integral from 0 to 3 of ysqrt(x+2) ?

The integral from 0 to 3 of ysqrt(x+2) is (9sqrt(2+x))/2

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integral from 0 to 3 of ysqrt(x+2)

\int_{0}^{3} y x + 2 d y

\frac{9 2 + x}{2}

Solution steps

\int_{0}^{3} y x + 2 d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 + x \cdot \int_{0}^{3} y d y

Apply the Power Rule

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

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

Compute the boundaries:

\frac{9}{2}

= 2 + x \frac{9}{2}

Simplify

= \frac{9 2 + x}{2}

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What is the integral from 0 to 3 of ysqrt(x+2) ?
The integral from 0 to 3 of ysqrt(x+2) is (9sqrt(2+x))/2