What is the integral from 1 to 6 of sqrt(5x-5) ?

The integral from 1 to 6 of sqrt(5x-5) is 50/3

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integral from 1 to 6 of sqrt(5x-5)

\int_{1}^{6} 5 x - 5 d x

\frac{50}{3}

Decimal

16.66666 \dots

Solution steps

\int_{1}^{6} 5 x - 5 d x

Apply u-substitution

= \int_{0}^{25} \frac{u}{5} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int_{0}^{25} u d u

Apply the Power Rule

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{25}

Compute the boundaries:

\frac{250}{3}

= \frac{1}{5} \cdot \frac{250}{3}

Simplify

= \frac{50}{3}

What is the integral from 1 to 6 of sqrt(5x-5) ?
The integral from 1 to 6 of sqrt(5x-5) is 50/3