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Popular >

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

Solution

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

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

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

Expand

x (1 - x) : x - x^{2}

= \int_{0}^{2} x - x^{2} 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

= \int_{0}^{2} x d x - \int_{0}^{2} x^{2} d x

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

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

= 2 - \frac{8}{3}

Simplify

2 - \frac{8}{3} : - \frac{2}{3}

= - \frac{2}{3}

Popular Examples

limit as x approaches-infinity of 1+e^x

x \to - \infty lim (1 + e^{x})

derivative of y^2+x

\frac{d}{d x} (y^{2} + x)

derivative of (-e^xx+2e^x/((1-x)^2))

\frac{d}{d x} (\frac{- e ^{x} x + 2 e ^{x}}{( 1 - x ) ^{2}})

taylor sin(3x), pi/3 taylor

sin (3 x), \frac{π}{3}

(dy)/(dx)= x/(y^2sqrt(1+x))

\frac{d y}{d x} = \frac{x}{y ^{2} 1 + x}

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x(1-x) ?
The integral from 0 to 2 of x(1-x) is -2/3