What is the integral from 0 to 1 of pi|x^4-x| ?

The integral from 0 to 1 of pi|x^4-x| is pi 3/10

Popular >

integral from 0 to 1 of pi|x^4-x|

\int_{0}^{1} π x^{4} - x d x

π \frac{3}{10}

Decimal Notation

0.94247 \dots

Solution steps

\int_{0}^{1} π x^{4} - x d x

Eliminate Absolutes

= \int_{0}^{1} π (- x^{4} + x) d x

Take the constant out:

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

= π \cdot \int_{0}^{1} - x^{4} + x 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}^{1} x^{4} d x + \int_{0}^{1} x d x)

\int_{0}^{1} x^{4} d x = \frac{1}{5}

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

= π (- \frac{1}{5} + \frac{1}{2})

Join

- \frac{1}{5} + \frac{1}{2} : \frac{3}{10}

= π \frac{3}{10}

\int_{0}^{1} (11 ln (x)) d x

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

\int_{0}^{1} 4 x (1 - x^{2}) d x

\int_{0}^{7} t e^{t} d t

\int_{1}^{s i n (x)} cos (x) d x

What is the integral from 0 to 1 of pi|x^4-x| ?
The integral from 0 to 1 of pi|x^4-x| is pi 3/10