What is the integral from 4 to 5 of (2+2x)^2 ?

The integral from 4 to 5 of (2+2x)^2 is 364/3

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integral from 4 to 5 of (2+2x)^2

\int_{4}^{5} (2 + 2 x)^{2} d x

\frac{364}{3}

Decimal

121.33333 \dots

Solution steps

\int_{4}^{5} (2 + 2 x)^{2} d x

Apply u-substitution

: \int_{10}^{12} \frac{u ^{2}}{2} d u

= \int_{10}^{12} \frac{u ^{2}}{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_{10}^{12} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{10}^{12}

= \frac{1}{2} [\frac{u ^{3}}{3}]_{10}^{12}

Compute the boundaries:

\frac{728}{3}

= \frac{1}{2} \cdot \frac{728}{3}

Simplify

= \frac{364}{3}

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What is the integral from 4 to 5 of (2+2x)^2 ?
The integral from 4 to 5 of (2+2x)^2 is 364/3