What is the integral from-pi to pi of cos^2(9x) ?

The integral from-pi to pi of cos^2(9x) is pi

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integral from-pi to pi of cos^2(9x)

\int_{- π}^{π} cos^{2} (9 x) d x

π

Decimal Notation

3.14159 \dots

Solution steps

\int_{- π}^{π} cos^{2} (9 x) d x

Rewrite using trig identities

= \int_{- π}^{π} \frac{1}{2} (1 + cos (18 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 (18 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 (18 x) d x)

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (18 x) d x = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\int \frac{cos ( a x )}{sin ^{5} ( a x )} d x

7 t sin (2 t)

\frac{d}{d x} (x y e^{\frac{- x ^{2}}{2} - \frac{y ^{2}}{2}})

\int r 9 - r^{2} d r

x^{^{'}} + (2 sin (t) cos (t)) x = e^{- s i n^{2} (t)}

What is the integral from-pi to pi of cos^2(9x) ?
The integral from-pi to pi of cos^2(9x) is pi