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

The integral from 0 to 3 of (x-3)^3 is -81/4

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

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

- \frac{81}{4}

Decimal

- 20.25

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{- 3}^{0}

= [\frac{u ^{4}}{4}]_{- 3}^{0}

Compute the boundaries:

- \frac{81}{4}

= - \frac{81}{4}

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What is the integral from 0 to 3 of (x-3)^3 ?
The integral from 0 to 3 of (x-3)^3 is -81/4