What is the integral from 1 to 9 of sqrt(6x-5) ?

The integral from 1 to 9 of sqrt(6x-5) is 38

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integral from 1 to 9 of sqrt(6x-5)

\int_{1}^{9} 6 x - 5 d x

38

Solution steps

\int_{1}^{9} 6 x - 5 d x

Apply u-substitution

= \int_{1}^{49} \frac{u}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{1}^{49} u d u

Apply the Power Rule

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{49}

Compute the boundaries:

228

= \frac{1}{6} \cdot 228

Simplify

= 38

What is the integral from 1 to 9 of sqrt(6x-5) ?
The integral from 1 to 9 of sqrt(6x-5) is 38