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

The integral from 2 to k of sqrt(x-2) is (2(k-2)^{3/2})/3

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integral from 2 to k of sqrt(x-2)

\int_{2}^{k} x - 2 d x

\frac{2 ( k - 2 ) ^{\frac{3}{2}}}{3}

Solution steps

\int_{2}^{k} x - 2 d x

Apply u-substitution

= \int_{0}^{k - 2} u d u

Apply the Power Rule

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

Compute the boundaries:

\frac{2}{3} (k - 2)^{\frac{3}{2}}

= \frac{2}{3} (k - 2)^{\frac{3}{2}}

Simplify

= \frac{2 ( k - 2 ) ^{\frac{3}{2}}}{3}

What is the integral from 2 to k of sqrt(x-2) ?
The integral from 2 to k of sqrt(x-2) is (2(k-2)^{3/2})/3