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Popular >

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

Solution

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

Solution

- \frac{2}{3}

+1

Decimal

- 0.66666 \dots

Solution steps

\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}

Graph

Popular Examples

integral from 0 to 2x^2 of tln(t)

\int_{0}^{2 x^{2}} t ln (t) d t

integral from 1 to 8 of \sqrt[3]{x}-1

\int_{1}^{8} 3 x - 1 d x

integral from 1 to 8 of 1+x^3

\int_{1}^{8} 1 + x^{3} d x

integral from x/2 to 2x-(x^2)/4 of 1

\int_{\frac{x}{2}}^{2 x - \frac{x ^{2}}{4}} 1

integral from 1 to t of 2x

\int_{1}^{t} 2 x d x

Frequently Asked Questions (FAQ)

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