What is the integral from 2 to 7 of sqrt(3x-1) ?

The integral from 2 to 7 of sqrt(3x-1) is (70sqrt(5))/9

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integral from 2 to 7 of sqrt(3x-1)

\int_{2}^{7} 3 x - 1 d x

\frac{70 5}{9}

Decimal Notation

17.39163 \dots

Solution steps

\int_{2}^{7} 3 x - 1 d x

Apply u-substitution

: \int_{5}^{20} \frac{u}{3} d u

= \int_{5}^{20} \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{5}^{20} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{20}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{20}

Compute the boundaries:

\frac{70 5}{3}

= \frac{1}{3} \cdot \frac{70 5}{3}

Simplify

= \frac{70 5}{9}

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What is the integral from 2 to 7 of sqrt(3x-1) ?
The integral from 2 to 7 of sqrt(3x-1) is (70sqrt(5))/9