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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{4}{3}

+1

Decimal

- 1.33333 \dots

Solution steps

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

Expand

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

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

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

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

= \frac{8}{3} - 4

Simplify

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

= - \frac{4}{3}

Graph

Popular Examples

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\int_{0}^{4} (4 x^{2} + x^{\frac{3}{2}}) d x

integral from 1 to 3 of x/(x+1)

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

integral from-2 to 3 of 8x^3+4x^2-7

\int_{- 2}^{3} 8 x^{3} + 4 x^{2} - 7 d x

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\int_{- 9}^{9} ∣ x ∣ d x

integral from 0 to x of x/8

\int_{0}^{x} \frac{x}{8} 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 -4/3