What is the integral from 0 to 7 of 3sqrt(x+9) ?

The integral from 0 to 7 of 3sqrt(x+9) is 74

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integral from 0 to 7 of 3sqrt(x+9)

\int_{0}^{7} 3 x + 9 d x

74

Solution steps

\int_{0}^{7} 3 x + 9 d x

Take the constant out:

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

= 3 \cdot \int_{0}^{7} x + 9 d x

Apply u-substitution

: \int_{9}^{16} u d u

= 3 \cdot \int_{9}^{16} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{16}

= 3 [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{16}

Compute the boundaries:

\frac{74}{3}

= 3 \cdot \frac{74}{3}

Simplify

= 74

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What is the integral from 0 to 7 of 3sqrt(x+9) ?
The integral from 0 to 7 of 3sqrt(x+9) is 74