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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-pi to pi of (pi^2-x^2)

\int_{- π}^{π} (π^{2} - x^{2}) d x

2 π^{3} - \frac{2 π ^{3}}{3}

Decimal Notation

41.34170 \dots

Solution steps

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

\int_{- π}^{π} π^{2} d x = 2 π^{3}

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

= 2 π^{3} - \frac{2 π ^{3}}{3}

\int_{0}^{2 π} 2 cos^{2} (x) d x

\int_{0}^{1} e^{- t} d t

\int_{0}^{1} x cos (x^{3}) d x

\int_{1}^{x} \frac{1}{x ^{2}} d x

\int_{0}^{\frac{π}{2}} sin (2 θ) d θ

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