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

The integral from 2 to 5 of sqrt(x-1) is 14/3

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

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

\frac{14}{3}

Decimal

4.66666 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{4} u d u

= \int_{1}^{4} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4}

= [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

\frac{14}{3}

= \frac{14}{3}

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\int_{1}^{3} \frac{12 ( ln ( x ) ) ^{5}}{x} d x

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{8}} d x

What is the integral from 2 to 5 of sqrt(x-1) ?
The integral from 2 to 5 of sqrt(x-1) is 14/3