What is the integral from 0 to 28 of sqrt(1+9/4 x) ?

The integral from 0 to 28 of sqrt(1+9/4 x) is 4088/27

Popular >

integral from 0 to 28 of sqrt(1+9/4 x)

\int_{0}^{28} 1 + \frac{9}{4} x d x

\frac{4088}{27}

Decimal

151.40740 \dots

Solution steps

\int_{0}^{28} 1 + \frac{9}{4} x d x

Apply u-substitution

: \int_{1}^{64} \frac{4 u}{9} d u

= \int_{1}^{64} \frac{4 u}{9} d u

Take the constant out:

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

= \frac{4}{9} \cdot \int_{1}^{64} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{64}

= \frac{4}{9} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{64}

Compute the boundaries:

\frac{1022}{3}

= \frac{4}{9} \cdot \frac{1022}{3}

Simplify

= \frac{4088}{27}

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

\int_{3}^{5} (x - 3)^{4} (5 - x)^{2} d x

\int_{- 1}^{34} x + 2 d x

\int_{- 0.1}^{0.9} - 1600 x d x

\int_{0}^{1} (4 - 8 v^{3} + 16 v^{7}) d v

What is the integral from 0 to 28 of sqrt(1+9/4 x) ?
The integral from 0 to 28 of sqrt(1+9/4 x) is 4088/27