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

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

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integral from 2 to 3 of sqrt(x-1)

\int_{2}^{3} x - 1 d x

\frac{4 2 - 2}{3}

Decimal

1.21895 \dots

Solution steps

\int_{2}^{3} x - 1 d x

Apply u-substitution

: \int_{1}^{2} u d u

= \int_{1}^{2} u d u

Apply the Power Rule

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

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

Compute the boundaries:

\frac{4 2}{3} - \frac{2}{3}

= \frac{4 2}{3} - \frac{2}{3}

Simplify

= \frac{4 2 - 2}{3}

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