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Popular >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

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

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

= 1 - \frac{1}{3}

Simplify

1 - \frac{1}{3} : \frac{2}{3}

= \frac{2}{3}

Graph

Popular Examples

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\int_{0}^{1} v (u + v^{2})^{4} d u

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\int_{2}^{7} \frac{12 x}{x ^{2} + 1} d x

integral from 0 to 1 of 5(1+x^2)^{-3/2}

\int_{0}^{1} 5 (1 + x^{2})^{- \frac{3}{2}} d x

integral from 1 to 6 of 4

\int_{1}^{6} 4 d x

integral from 0 to 4 of 1/(64-x^3)

\int_{0}^{4} \frac{1}{64 - x ^{3}} d x

Frequently Asked Questions (FAQ)

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