What is the integral from 0 to 2 of (x+1)^3 ?

The integral from 0 to 2 of (x+1)^3 is 20

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integral from 0 to 2 of (x+1)^3

\int_{0}^{2} (x + 1)^{3} d x

20

Solution steps

\int_{0}^{2} (x + 1)^{3} d x

Apply u-substitution

: \int_{1}^{3} u^{3} d u

= \int_{1}^{3} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{1}^{3}

= [\frac{u ^{4}}{4}]_{1}^{3}

Compute the boundaries:

20

= 20

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What is the integral from 0 to 2 of (x+1)^3 ?
The integral from 0 to 2 of (x+1)^3 is 20