What is the integral from 2.5 to 0.5 of (23.75-7.5v) ?

The integral from 2.5 to 0.5 of (23.75-7.5v) is -25

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2.5 to 0.5 of (23.75-7.5v)

\int_{2.5}^{0.5} (23.75 - 7.5 v) d v

- 25

Solution steps

\int_{2.5}^{0.5} 23.75 - 7.5 v d v

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0.5}^{2.5} 23.75 - 7.5 v d v

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (\int_{0.5}^{2.5} 23.75 d v - \int_{0.5}^{2.5} 7.5 v d v)

\int_{0.5}^{2.5} 23.75 d v = 47.5

\int_{0.5}^{2.5} 7.5 v d v = 22.5

= - (47.5 - 22.5)

Simplify

= - 25

What is the integral from 2.5 to 0.5 of (23.75-7.5v) ?
The integral from 2.5 to 0.5 of (23.75-7.5v) is -25