What is the integral from 0 to 2 of 8r^2-2r^4 ?

The integral from 0 to 2 of 8r^2-2r^4 is 128/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of 8r^2-2r^4

\int_{0}^{2} 8 r^{2} - 2 r^{4} d r

\frac{128}{15}

Decimal Notation

8.53333 \dots

Solution steps

\int_{0}^{2} 8 r^{2} - 2 r^{4} d r

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}^{2} 8 r^{2} d r - \int_{0}^{2} 2 r^{4} d r

\int_{0}^{2} 8 r^{2} d r = \frac{64}{3}

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

= \frac{64}{3} - \frac{64}{5}

Simplify

\frac{64}{3} - \frac{64}{5} : \frac{128}{15}

= \frac{128}{15}

\int_{4}^{14} 5 e^{0.02 t} d t

\int_{0}^{8} \frac{x}{36 + x ^{2}} d x

\int_{1}^{4} e^{2 x} d x

\int_{0}^{π} π^{2} - x^{2} d x

\int_{- 1}^{0} ∣ x ∣ d x

What is the integral from 0 to 2 of 8r^2-2r^4 ?
The integral from 0 to 2 of 8r^2-2r^4 is 128/15