en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1-x^2)

Solution

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

Solution

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

Solution steps

\int 1 - 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 1 d x - \int x^{2} d x

\int 1 d x = x

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of sin(x)sin(t-x)

\int sin (x) sin (t - x) d x

area y=x^7,0,4 area

y = x^{7}, 0, 4

integral of 1/((3-5x)^2)

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

integral of (x^2)/(sqrt(81-x^2))

\int \frac{x ^{2}}{81 - x ^{2}} d x

integral of 1/(x(1+x^3))

\int \frac{1}{x ( 1 + x ^{3} )} d x

Frequently Asked Questions (FAQ)

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