What is the integral from 0 to 1 of ax+bx^2 ?

The integral from 0 to 1 of ax+bx^2 is a/2+b/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of ax+bx^2

\int_{0}^{1} a x + b x^{2} d x

\frac{a}{2} + \frac{b}{3}

Solution steps

\int_{0}^{1} a x + b 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}^{1} a x d x + \int_{0}^{1} b x^{2} d x

\int_{0}^{1} a x d x = \frac{a}{2}

\int_{0}^{1} b x^{2} d x = \frac{b}{3}

= \frac{a}{2} + \frac{b}{3}

What is the integral from 0 to 1 of ax+bx^2 ?
The integral from 0 to 1 of ax+bx^2 is a/2+b/3