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

The integral from 2 to 5 of (2+2y)^2 is 252

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integral from 2 to 5 of (2+2y)^2

\int_{2}^{5} (2 + 2 y)^{2} d y

252

Solution steps

\int_{2}^{5} (2 + 2 y)^{2} d y

Apply u-substitution

: \int_{6}^{12} \frac{u ^{2}}{2} d u

= \int_{6}^{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_{6}^{12} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{6}^{12}

= \frac{1}{2} [\frac{u ^{3}}{3}]_{6}^{12}

Compute the boundaries:

504

= \frac{1}{2} \cdot 504

Simplify

= 252

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What is the integral from 2 to 5 of (2+2y)^2 ?
The integral from 2 to 5 of (2+2y)^2 is 252