What is the integral from 0 to 5 of 10+4x-x^2 ?

The integral from 0 to 5 of 10+4x-x^2 is 175/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 5 of 10+4x-x^2

\int_{0}^{5} 10 + 4 x - x^{2} d x

\frac{175}{3}

Decimal

58.33333 \dots

Solution steps

\int_{0}^{5} 10 + 4 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}^{5} 10 d x + \int_{0}^{5} 4 x d x - \int_{0}^{5} x^{2} d x

\int_{0}^{5} 10 d x = 50

\int_{0}^{5} 4 x d x = 50

\int_{0}^{5} x^{2} d x = \frac{125}{3}

= 50 + 50 - \frac{125}{3}

Simplify

50 + 50 - \frac{125}{3} : \frac{175}{3}

= \frac{175}{3}

\int_{1}^{3} 3^{x} d x

\int_{0}^{\frac{π}{2}} e^{x} - sin (x) d x

\int_{- 2}^{2} cos (x) d x

\int_{1}^{3} 12 x^{2} d x

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

What is the integral from 0 to 5 of 10+4x-x^2 ?
The integral from 0 to 5 of 10+4x-x^2 is 175/3