What is the integral from-pi to pi of cos^2(5x) ?

The integral from-pi to pi of cos^2(5x) is pi

Popular >

integral from-pi to pi of cos^2(5x)

\int_{- π}^{π} cos^{2} (5 x) d x

π

Decimal Notation

3.14159 \dots

Solution steps

\int_{- π}^{π} cos^{2} (5 x) d x

Rewrite using trig identities

= \int_{- π}^{π} \frac{1}{2} (1 + cos (10 x)) 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 (10 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 (10 x) d x)

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (10 x) d x = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

x \to \frac{π}{2} + lim (\frac{1}{x} sec (x))

\int sec (38 w) tan (38 w) d w

x \to 1 lim (∣ x - 2 ∣)

\int tan (x) sec^{3} (x) d x

\int \frac{x}{x + d} d x

What is the integral from-pi to pi of cos^2(5x) ?
The integral from-pi to pi of cos^2(5x) is pi