What is the integral from 0 to 1 of sqrt(3x+5) ?

The integral from 0 to 1 of sqrt(3x+5) is (32sqrt(2)-10sqrt(5))/9

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integral from 0 to 1 of sqrt(3x+5)

\int_{0}^{1} 3 x + 5 d x

\frac{32 2 - 10 5}{9}

Decimal

2.54379 \dots

Solution steps

\int_{0}^{1} 3 x + 5 d x

Apply u-substitution

= \int_{5}^{8} \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}^{8} u d u

Apply the Power Rule

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{8}

Compute the boundaries:

\frac{32 2 - 10 5}{3}

= \frac{1}{3} \cdot \frac{32 2 - 10 5}{3}

Simplify

= \frac{32 2 - 10 5}{9}

What is the integral from 0 to 1 of sqrt(3x+5) ?
The integral from 0 to 1 of sqrt(3x+5) is (32sqrt(2)-10sqrt(5))/9