en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of 2x-2x^2

Solution

\int 2 x - 2 x^{2} d x

Solution

x^{2} - \frac{2 x ^{3}}{3} + C

Solution steps

\int 2 x - 2 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 2 x d x - \int 2 x^{2} d x

\int 2 x d x = x^{2}

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

= x^{2} - \frac{2 x ^{3}}{3}

Add a constant to the solution

= x^{2} - \frac{2 x ^{3}}{3} + C

Graph

Popular Examples

area f(x)=x^2,g(x)=2x

integral of 3/(80-t)

integral from-2 to 1 of x^2+x-2

integral of (2x(x^2+2)^2)

derivative of tsin(t)+cos(t)

Frequently Asked Questions (FAQ)

What is the integral of 2x-2x^2 ?
The integral of 2x-2x^2 is x^2-(2x^3)/3+C