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Popular >

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

Solution

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

Solution

\frac{2}{3}

+1

Decimal

0.66666 \dots

Solution steps

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

Expand

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

= \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

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\int_{0}^{2 π} sin^{4} (θ) d θ

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

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\int_{0}^{π} cos^{3} (x) sin (x) d x

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\int_{0}^{t} 3 e^{x} d x

Frequently Asked Questions (FAQ)

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