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

The integral from 0 to 1 of sqrt(5x+3) is (32sqrt(2)-6sqrt(3))/(15)

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

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

\frac{32 2 - 6 3}{15}

Decimal

2.32416 \dots

Solution steps

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

Apply u-substitution

: \int_{3}^{8} \frac{u}{5} d u

= \int_{3}^{8} \frac{u}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{3}^{8} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{8}

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

Compute the boundaries:

\frac{32 2}{3} - 23

= \frac{1}{5} (\frac{32 2}{3} - 23)

Simplify

= \frac{32 2 - 6 3}{15}

\int_{0}^{2} 2 x^{3} + 3 d x

\int_{- \frac{π}{2}}^{π} cos (x) d x

\int_{- 2}^{0} - cos (\frac{nπ x}{2}) d x

\int_{1}^{1} x^{3} d x

\int_{- 1}^{2} (x - 1)^{2} + 1 d x

What is the integral from 0 to 1 of sqrt(5x+3) ?
The integral from 0 to 1 of sqrt(5x+3) is (32sqrt(2)-6sqrt(3))/(15)