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Popular >

integral from 0 to 2 of x(x-3)

Solution

\int_{0}^{2} x (x - 3) d x

Solution

- \frac{10}{3}

+1

Decimal

- 3.33333 \dots

Solution steps

\int_{0}^{2} x (x - 3) d x

Expand

x (x - 3) : x^{2} - 3 x

= \int_{0}^{2} x^{2} - 3 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} 3 x d x

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

\int_{0}^{2} 3 x d x = 6

= \frac{8}{3} - 6

Simplify

\frac{8}{3} - 6 : - \frac{10}{3}

= - \frac{10}{3}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x(x-3) ?
The integral from 0 to 2 of x(x-3) is -10/3