What is the integral from 1 to 2 of sqrt(5x-1) ?

The integral from 1 to 2 of sqrt(5x-1) is 38/15

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integral from 1 to 2 of sqrt(5x-1)

\int_{1}^{2} 5 x - 1 d x

\frac{38}{15}

Decimal

2.53333 \dots

Solution steps

\int_{1}^{2} 5 x - 1 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_{- \infty}^{3} \frac{1}{x ^{2} + 9} d x

\frac{\partial}{\partial y} (\frac{6 x}{3 x ^{2} - y ^{3} - 3})

\frac{d}{d x} ((x - 1)^{2} \cdot (x - 2) \cdot (x - 4))

x^{7} - 3 x^{4} + 7 x^{3} + 43, at x = - 2

\int \frac{1}{x 1 + x} d x

What is the integral from 1 to 2 of sqrt(5x-1) ?
The integral from 1 to 2 of sqrt(5x-1) is 38/15