What is the integral from 1 to 2 of (x-2)^5 ?

The integral from 1 to 2 of (x-2)^5 is -1/6

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integral from 1 to 2 of (x-2)^5

\int_{1}^{2} (x - 2)^{5} d x

- \frac{1}{6}

Solution steps

\int_{1}^{2} (x - 2)^{5} d x

Apply u-substitution

: \int_{- 1}^{0} u^{5} d u

= \int_{- 1}^{0} u^{5} d u

Apply the Power Rule

: [\frac{u ^{6}}{6}]_{- 1}^{0}

= [\frac{u ^{6}}{6}]_{- 1}^{0}

Compute the boundaries:

- \frac{1}{6}

= - \frac{1}{6}

\int_{- 5}^{- 3} - x^{2} - 3 x d x

\int_{0}^{4} (3 x + 4) d x

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

\int_{0}^{1} x (e^{x} - 1) d x

\int_{2}^{4} 3^{5 x} d x

What is the integral from 1 to 2 of (x-2)^5 ?
The integral from 1 to 2 of (x-2)^5 is -1/6