What is the integral from 1 to 2 of sqrt(18x+37) ?

The integral from 1 to 2 of sqrt(18x+37) is (73sqrt(73)-55sqrt(55))/(27)

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integral from 1 to 2 of sqrt(18x+37)

\int_{1}^{2} 18 x + 37 d x

\frac{73 73 - 55 55}{27}

Decimal Notation

7.99338 \dots

Solution steps

\int_{1}^{2} 18 x + 37 d x

Apply u-substitution

: \int_{55}^{73} \frac{u}{18} d u

= \int_{55}^{73} \frac{u}{18} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int_{55}^{73} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{55}^{73}

= \frac{1}{18} [\frac{2}{3} u^{\frac{3}{2}}]_{55}^{73}

Compute the boundaries:

\frac{146 73 - 110 55}{3}

= \frac{1}{18} \cdot \frac{146 73 - 110 55}{3}

Simplify

= \frac{73 73 - 55 55}{27}

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What is the integral from 1 to 2 of sqrt(18x+37) ?
The integral from 1 to 2 of sqrt(18x+37) is (73sqrt(73)-55sqrt(55))/(27)