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

The integral from-pi to pi of cos(x)cos(x) is pi

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 cos(x)cos(x)

\int_{- π}^{π} cos (x) cos (x) d x

π

Decimal

3.14159 \dots

Solution steps

\int_{- π}^{π} cos (x) cos (x) d x

Simplify

cos (x) cos (x) : cos^{2} (x)

= \int_{- π}^{π} cos^{2} (x) d x

Rewrite using trig identities

= \int_{- π}^{π} \frac{1 + cos ( 2 x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- π}^{π} 1 + cos (2 x) 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

= \frac{1}{2} (\int_{- π}^{π} 1 d x + \int_{- π}^{π} cos (2 x) d x)

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (2 x) d x = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\int_{0}^{3} y d y

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

\int_{3}^{5} \frac{1}{x ^{2} - 3 x + 2} d x

\int_{0}^{2} x^{3} - 5 x^{2} + 6 x d x

\int_{1}^{2} 6 x^{4} d x

What is the integral from-pi to pi of cos(x)cos(x) ?
The integral from-pi to pi of cos(x)cos(x) is pi