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

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

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

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

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

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

Apply u-substitution

: \int_{- 3}^{- 2} \frac{1}{u ^{2}} d u

= \int_{- 3}^{- 2} \frac{1}{u ^{2}} d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{6}

= \frac{1}{6}

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\int_{0}^{4} \frac{3}{16} x d x

\int_{1}^{2} \frac{1}{2 x} d x

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