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

The integral from 0 to 2 of (x-2)^3 is -4

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

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

- 4

Solution steps

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

Apply u-substitution

: \int_{- 2}^{0} u^{3} d u

= \int_{- 2}^{0} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{- 2}^{0}

= [\frac{u ^{4}}{4}]_{- 2}^{0}

Compute the boundaries:

- 4

= - 4

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