What is the integral from 0 to a of ax-x^2 ?

The integral from 0 to a of ax-x^2 is (a^3)/2-(a^3)/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to a of ax-x^2

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

\frac{a ^{3}}{2} - \frac{a ^{3}}{3}

Solution steps

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

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

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

= \frac{a ^{3}}{2} - \frac{a ^{3}}{3}

\int_{- 3}^{0} 18 x + 55 d x

\int_{- 5}^{0} sin (\frac{nπ x}{5}) d x

\int_{1}^{2} [\frac{in x}{x ^{2}}] d x

\int_{0}^{t} sin (t - u) sin (u) d u

\int_{- 2}^{1} 6 - x^{2} d x

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