What is the integral from 0 to 2 of pi(2x^2-x^4) ?

The integral from 0 to 2 of pi(2x^2-x^4) is -pi 16/15

Popular >

integral from 0 to 2 of pi(2x^2-x^4)

\int_{0}^{2} π (2 x^{2} - x^{4}) d x

- π \frac{16}{15}

Decimal

- 3.35103 \dots

Solution steps

\int_{0}^{2} π (2 x^{2} - x^{4}) d x

Take the constant out:

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

= π \cdot \int_{0}^{2} 2 x^{2} - x^{4} 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

= π (\int_{0}^{2} 2 x^{2} d x - \int_{0}^{2} x^{4} d x)

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} x^{4} d x = \frac{32}{5}

= π (\frac{16}{3} - \frac{32}{5})

Simplify

π (\frac{16}{3} - \frac{32}{5}) : - π \frac{16}{15}

= - π \frac{16}{15}

\int_{0}^{\frac{1}{4}} 2 x d x

\int_{1}^{9} \frac{2}{t} d t

\int_{- 4}^{8} (10 - x) d x

\int_{0.25}^{0.6} 4 (1 - y)^{3} d y

\int_{2}^{5} (4 x - 3)^{9} d x

What is the integral from 0 to 2 of pi(2x^2-x^4) ?
The integral from 0 to 2 of pi(2x^2-x^4) is -pi 16/15