What is the integral from 0 to 1 of pi(x^2-x) ?

The integral from 0 to 1 of pi(x^2-x) is -pi/6

Popular >

integral from 0 to 1 of pi(x^2-x)

\int_{0}^{1} π (x^{2} - x) d x

- \frac{π}{6}

Decimal Notation

- 0.52359 \dots

Solution steps

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

\int_{0}^{1} x^{2} d x = \frac{1}{3}

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

= π (\frac{1}{3} - \frac{1}{2})

Simplify

π (\frac{1}{3} - \frac{1}{2}) : - \frac{π}{6}

= - \frac{π}{6}

\int_{0}^{1} \frac{( 1 + e ^{x} )}{e ^{x}} d x

\int \frac{x ^{2}}{9 - 4 x ^{2}} d x

\frac{d}{d x} (a^{x} \cdot x^{a})

x + 2 x y^{2} + e^{x^{2}} y \frac{d y}{d x} = 0

\int 2 (y - 1) d y

What is the integral from 0 to 1 of pi(x^2-x) ?
The integral from 0 to 1 of pi(x^2-x) is -pi/6