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Popular Calculus >

integral from 0 to 2 of x(x-4)

Solution

\int_{0}^{2} x (x - 4) d x

Solution

- \frac{16}{3}

+1

Decimal

- 5.33333 \dots

Solution steps

\int_{0}^{2} x (x - 4) d x

Expand

x (x - 4) : x^{2} - 4 x

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

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

\int_{0}^{2} 4 x d x = 8

= \frac{8}{3} - 8

Simplify

\frac{8}{3} - 8 : - \frac{16}{3}

= - \frac{16}{3}

Graph

Popular Examples

integral from 1 to 2 of 1/(x^2)sin(1/x)

\int_{1}^{2} \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

integral from 3 to x^3 of ln(x)

\int_{3}^{x^{3}} ln (x) d x

integral from 0 to 1 of te^{(-t^2)/2}

\int_{0}^{1} t e^{\frac{- t ^{2}}{2}} d t

integral from 1 to tan(5x) of sqrt(1-t)

\int_{1}^{t a n (5 x)} 1 - t d t

integral from 0 to 4 of r

\int_{0}^{4} r d r

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x(x-4) ?
The integral from 0 to 2 of x(x-4) is -16/3