What is the integral from-3 to 0 of sqrt(18x+55) ?

The integral from-3 to 0 of sqrt(18x+55) is (55sqrt(55)-1)/(27)

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integral from-3 to 0 of sqrt(18x+55)

\int_{- 3}^{0} 18 x + 55 d x

\frac{55 55 - 1}{27}

Decimal Notation

15.07003 \dots

Solution steps

\int_{- 3}^{0} 18 x + 55 d x

Apply u-substitution

: \int_{1}^{55} \frac{u}{18} d u

= \int_{1}^{55} \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_{1}^{55} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{55}

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

Compute the boundaries:

\frac{110 55}{3} - \frac{2}{3}

= \frac{1}{18} (\frac{110 55}{3} - \frac{2}{3})

Simplify

= \frac{55 55 - 1}{27}

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What is the integral from-3 to 0 of sqrt(18x+55) ?
The integral from-3 to 0 of sqrt(18x+55) is (55sqrt(55)-1)/(27)