What is the integral from 0 to 4 of [(5x-x^2)-x] ?

The integral from 0 to 4 of [(5x-x^2)-x] is 32/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 4 of [(5x-x^2)-x]

\int_{0}^{4} [(5 x - x^{2}) - x] d x

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

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

Simplify

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

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 4 x d x = 32

= - \frac{64}{3} + 32

Simplify

- \frac{64}{3} + 32 : \frac{32}{3}

= \frac{32}{3}

\int_{- 4}^{0} (4 x - e^{x}) d x

\int_{- 1}^{0} (x + 1) cos (nπ x) d x

\int_{1}^{3} (x^{2} - x) d x

\int_{0}^{π} x \cdot cos (x^{2}) d x

\int_{7}^{49} \frac{1}{x ( ln ( x ) ) ^{4}} d x

What is the integral from 0 to 4 of [(5x-x^2)-x] ?
The integral from 0 to 4 of [(5x-x^2)-x] is 32/3