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

The integral from 1 to 3 of sqrt(7x+2) is (46sqrt(23)-54)/(21)

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

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

\frac{46 23 - 54}{21}

Decimal

7.93372 \dots

Solution steps

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

Apply u-substitution

= \int_{9}^{23} \frac{u}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{9}^{23} u d u

Apply the Power Rule

= \frac{1}{7} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{23}

Compute the boundaries:

\frac{46 23}{3} - 18

= \frac{1}{7} (\frac{46 23}{3} - 18)

Simplify

= \frac{46 23 - 54}{21}

What is the integral from 1 to 3 of sqrt(7x+2) ?
The integral from 1 to 3 of sqrt(7x+2) is (46sqrt(23)-54)/(21)