What is the integral from-1 to 1 of 1/((x-2)^3) ?

The integral from-1 to 1 of 1/((x-2)^3) is -4/9

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integral from-1 to 1 of 1/((x-2)^3)

\int_{- 1}^{1} \frac{1}{( x - 2 ) ^{3}} d x

- \frac{4}{9}

Decimal

- 0.44444 \dots

Solution steps

\int_{- 1}^{1} \frac{1}{( x - 2 ) ^{3}} d x

Apply u-substitution

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

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

Apply the Power Rule

: [- \frac{1}{2 u ^{2}}]_{- 3}^{- 1}

= [- \frac{1}{2 u ^{2}}]_{- 3}^{- 1}

Compute the boundaries:

- \frac{4}{9}

= - \frac{4}{9}

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What is the integral from-1 to 1 of 1/((x-2)^3) ?
The integral from-1 to 1 of 1/((x-2)^3) is -4/9