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

The integral from 0 to 2 of (x+2)^3 is 60

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

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

60

Solution steps

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

Apply u-substitution

: \int_{2}^{4} u^{3} d u

= \int_{2}^{4} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{2}^{4}

= [\frac{u ^{4}}{4}]_{2}^{4}

Compute the boundaries:

60

= 60

\int_{0}^{4} (x - \frac{x}{2}) d x

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

\int_{- 2}^{2} x 25 - x^{2} d x

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

\int_{4}^{16} x d x

What is the integral from 0 to 2 of (x+2)^3 ?
The integral from 0 to 2 of (x+2)^3 is 60