What is the integral of (2-1/2 x)^2 ?

The integral of (2-1/2 x)^2 is 4x-x^2+(x^3)/(12)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2-1/2 x)^2

\int (2 - \frac{1}{2} x)^{2} d x

4 x - x^{2} + \frac{x ^{3}}{12} + C

Solution steps

\int (2 - \frac{1}{2} x)^{2} d x

Simplify

(2 - \frac{1}{2} x)^{2} : 4 - 2 x + \frac{1}{4} x^{2}

= \int 4 - 2 x + \frac{1}{4} 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 4 d x - \int 2 x d x + \int \frac{1}{4} x^{2} d x

\int 4 d x = 4 x

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

\int \frac{1}{4} x^{2} d x = \frac{x ^{3}}{12}

= 4 x - x^{2} + \frac{x ^{3}}{12}

Add a constant to the solution

= 4 x - x^{2} + \frac{x ^{3}}{12} + C

\int 6 - \frac{6}{x ^{2}} d x

\int e^{- (3 x^{2} + 1)} x d x

\int x cos (\frac{nπ x}{20}) d x

\int \frac{sec ^{2} ( x )}{5 + 3 tan ( x )} d x

\int \frac{( x ^{2} - 1 )}{x - 1} d x

What is the integral of (2-1/2 x)^2 ?
The integral of (2-1/2 x)^2 is 4x-x^2+(x^3)/(12)+C