What is the integral from 0 to 1 of sqrt(x-1) ?

The integral from 0 to 1 of sqrt(x-1) is (2i)/3

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integral from 0 to 1 of sqrt(x-1)

\int_{0}^{1} x - 1 d x

\frac{2 i}{3}

Solution steps

\int_{0}^{1} x - 1 d x

Apply u-substitution

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

Apply the Power Rule

= [\frac{2}{3} u^{\frac{3}{2}}]_{- 1}^{0}

Compute the boundaries:

i \frac{2}{3}

= i \frac{2}{3}

Simplify

= \frac{2 i}{3}

What is the integral from 0 to 1 of sqrt(x-1) ?
The integral from 0 to 1 of sqrt(x-1) is (2i)/3