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

The integral from 4 to 9 of (1+x)sqrt(x) is 1456/15

Popular >

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

\int_{4}^{9} (1 + x) x d x

\frac{1456}{15}

Decimal

97.06666 \dots

Solution steps

\int_{4}^{9} (1 + x) x d x

Expand

(1 + x) x : x + x^{\frac{3}{2}}

= \int_{4}^{9} x + x^{\frac{3}{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{4}^{9} x d x + \int_{4}^{9} x^{\frac{3}{2}} d x

\int_{4}^{9} x d x = \frac{38}{3}

\int_{4}^{9} x^{\frac{3}{2}} d x = \frac{422}{5}

= \frac{38}{3} + \frac{422}{5}

Simplify

\frac{38}{3} + \frac{422}{5} : \frac{1456}{15}

= \frac{1456}{15}

\int_{0}^{4} (x + 3) d x

\int_{0}^{1} (e^{x} - 1)^{4} e^{x} d x

\int_{a}^{b} x \frac{1}{b - a} d x

\int_{1}^{6} \frac{9}{x} d x

\int_{0}^{2} x \cdot \frac{x}{2} d x

What is the integral from 4 to 9 of (1+x)sqrt(x) ?
The integral from 4 to 9 of (1+x)sqrt(x) is 1456/15