What is the integral from 0 to 1 of sqrt(2+5x) ?

The integral from 0 to 1 of sqrt(2+5x) is (14sqrt(7)-4sqrt(2))/(15)

integral from 0 to 1 of sqrt(2+5x)

\int_{0}^{1} 2 + 5 x d x

\frac{14 7 - 4 2}{15}

Decimal

2.09224 \dots

Solution steps

\int_{0}^{1} 2 + 5 x d x

Apply u-substitution

= \int_{2}^{7} \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_{2}^{7} u d u

Apply the Power Rule

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{7}

Compute the boundaries:

\frac{14 7 - 4 2}{3}

= \frac{1}{5} \cdot \frac{14 7 - 4 2}{3}

Simplify

= \frac{14 7 - 4 2}{15}

\int_{- \frac{π}{4}}^{0} sec (x) tan (x) d x

\int_{1}^{5} 7 - 2 x d x

\int_{1}^{4} (1 + \frac{1}{x} + \frac{1}{x ^{2}}) d x

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

\int_{0}^{t} (t - w) e^{5 w} d w

What is the integral from 0 to 1 of sqrt(2+5x) ?
The integral from 0 to 1 of sqrt(2+5x) is (14sqrt(7)-4sqrt(2))/(15)