What is the integral from 0 to 1 of sqrt(5x+4) ?

The integral from 0 to 1 of sqrt(5x+4) is 38/15

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integral from 0 to 1 of sqrt(5x+4)

\int_{0}^{1} 5 x + 4 d x

\frac{38}{15}

Decimal Notation

2.53333 \dots

Solution steps

\int_{0}^{1} 5 x + 4 d x

Apply u-substitution

: \int_{4}^{9} \frac{u}{5} d u

= \int_{4}^{9} \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_{4}^{9} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{9}

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{9}

Compute the boundaries:

\frac{38}{3}

= \frac{1}{5} \cdot \frac{38}{3}

Simplify

= \frac{38}{15}

\int_{0}^{x} 9 + x^{2} d x

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\int_{- 1}^{0} e^{x} cos (e^{x}) d x

What is the integral from 0 to 1 of sqrt(5x+4) ?
The integral from 0 to 1 of sqrt(5x+4) is 38/15