What is the integral from-3 to 0 of (2x+6)^4 ?

The integral from-3 to 0 of (2x+6)^4 is 3888/5

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integral from-3 to 0 of (2x+6)^4

\int_{- 3}^{0} (2 x + 6)^{4} d x

\frac{3888}{5}

Decimal

777.6

Solution steps

\int_{- 3}^{0} (2 x + 6)^{4} d x

Apply u-substitution

: \int_{0}^{6} \frac{u ^{4}}{2} d u

= \int_{0}^{6} \frac{u ^{4}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{6} u^{4} d u

Apply the Power Rule

: [\frac{u ^{5}}{5}]_{0}^{6}

= \frac{1}{2} [\frac{u ^{5}}{5}]_{0}^{6}

Compute the boundaries:

\frac{7776}{5}

= \frac{1}{2} \cdot \frac{7776}{5}

Simplify

= \frac{3888}{5}

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What is the integral from-3 to 0 of (2x+6)^4 ?
The integral from-3 to 0 of (2x+6)^4 is 3888/5