What is the integral from 0 to 2 of (10x-5x^2) ?

The integral from 0 to 2 of (10x-5x^2) is 20/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (10x-5x^2)

\int_{0}^{2} (10 x - 5 x^{2}) d x

\frac{20}{3}

Decimal Notation

6.66666 \dots

Solution steps

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

\int_{0}^{2} 10 x d x = 20

\int_{0}^{2} 5 x^{2} d x = \frac{40}{3}

= 20 - \frac{40}{3}

Simplify

20 - \frac{40}{3} : \frac{20}{3}

= \frac{20}{3}

\int \frac{1}{10 - 0.8 x} d x

y^{^{''}} - 10 y^{^{'}} + 25 y = 4 x e^{5 x}

\frac{\partial}{\partial x} (9 x e^{2 x y})

\frac{s ^{2} + 2 s + 5}{s ^{2} ( s + 1 )}

e^{i θ}

What is the integral from 0 to 2 of (10x-5x^2) ?
The integral from 0 to 2 of (10x-5x^2) is 20/3