What is the integral from 0 to 5 of (7x-x^2-2x) ?

The integral from 0 to 5 of (7x-x^2-2x) is 125/6

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 (7x-x^2-2x)

\int_{0}^{5} (7 x - x^{2} - 2 x) d x

\frac{125}{6}

Decimal Notation

20.83333 \dots

Solution steps

\int_{0}^{5} 7 x - x^{2} - 2 x d x

Simplify

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

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

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

= - \frac{125}{3} + \frac{125}{2}

Simplify

- \frac{125}{3} + \frac{125}{2} : \frac{125}{6}

= \frac{125}{6}

x y^{^{'}} = - y + 2 x^{2} y

\frac{d}{d x} (e \cdot ln (x))

\int e^{x + 5} (x^{2} + 3) d x

\frac{d}{d x} ((x^{2} + 5 x + 1) (x^{3} - 2 x))

y^{^{'}} + 4 y = - 1

What is the integral from 0 to 5 of (7x-x^2-2x) ?
The integral from 0 to 5 of (7x-x^2-2x) is 125/6