What is the integral from 0 to pi of pi^2-x^2 ?

The integral from 0 to pi of pi^2-x^2 is pi^3-(pi^3)/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 pi of pi^2-x^2

\int_{0}^{π} π^{2} - x^{2} d x

π^{3} - \frac{π ^{3}}{3}

Decimal

20.67085 \dots

Solution steps

\int_{0}^{π} π^{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_{0}^{π} π^{2} d x - \int_{0}^{π} x^{2} d x

\int_{0}^{π} π^{2} d x = π^{3}

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

= π^{3} - \frac{π ^{3}}{3}

\int_{0}^{1} x - 2 d x

\int_{1}^{e^{4}} x ln (x) d x

\int_{2}^{4} 9 x^{2} d x

\int_{0}^{\frac{π}{4}} 3 sin (x) d x

\int_{- 1}^{1} arcsin (x) d x

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