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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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})

Simplify

π (\frac{1}{5} - \frac{1}{2}) : - π \frac{3}{10}

= - π \frac{3}{10}

\frac{\partial}{\partial x} (e^{e^{y} x + y})

f (x) = 4 x^{2} + 6 x + 3

\int e^{- (x)^{2}} d x

\int 4 x sin (5 x) d x

\int x^{3} sin (5 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