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Popular Calculus >

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

Solution

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

Solution

\frac{4}{3}

+1

Decimal

1.33333 \dots

Solution steps

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

Expand

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

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

\int_{0}^{2} 2 x d x = 4

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

= 4 - \frac{8}{3}

Simplify

4 - \frac{8}{3} : \frac{4}{3}

= \frac{4}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x(2-x) ?
The integral from 0 to 2 of x(2-x) is 4/3