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

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

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integral from-pi to pi of cos^2(3x)

\int_{- π}^{π} cos^{2} (3 x) d x

π

Decimal Notation

3.14159 \dots

Solution steps

\int_{- π}^{π} cos^{2} (3 x) d x

Rewrite using trig identities

= \int_{- π}^{π} \frac{1}{2} (1 + cos (6 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 (6 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 (6 x) d x)

\int_{- π}^{π} 1 d x = 2 π

\int_{- π}^{π} cos (6 x) d x = 0

= \frac{1}{2} (2 π + 0)

Simplify

\frac{1}{2} (2 π + 0) : π

= π

\int_{- 1}^{22} 21 x - (x^{2} - 22) d x

\int 4 x + 2 d x

\frac{d}{d x} (\frac{1}{2} e^{x^{2}})

\frac{x ^{2}}{5 ( 1 - x )}

f (x) = 2 x^{2} + x - 1, at a = - 1

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