What is the integral from 0 to 4 of (4x^2+x^{3/2}) ?

The integral from 0 to 4 of (4x^2+x^{3/2}) is 1472/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 4 of (4x^2+x^{3/2})

\int_{0}^{4} (4 x^{2} + x^{\frac{3}{2}}) d x

\frac{1472}{15}

Decimal

98.13333 \dots

Solution steps

\int_{0}^{4} 4 x^{2} + 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_{0}^{4} 4 x^{2} d x + \int_{0}^{4} x^{\frac{3}{2}} d x

\int_{0}^{4} 4 x^{2} d x = \frac{256}{3}

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= \frac{256}{3} + \frac{64}{5}

Simplify

\frac{256}{3} + \frac{64}{5} : \frac{1472}{15}

= \frac{1472}{15}

\int_{1}^{3} \frac{x}{x + 1} d x

\int_{- 2}^{3} 8 x^{3} + 4 x^{2} - 7 d x

\int_{- 9}^{9} ∣ x ∣ d x

\int_{0}^{x} \frac{x}{8} d x

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

What is the integral from 0 to 4 of (4x^2+x^{3/2}) ?
The integral from 0 to 4 of (4x^2+x^{3/2}) is 1472/15