What is the integral from 0 to pi of cos(3x)cos(3x) ?

The integral from 0 to pi of cos(3x)cos(3x) is pi/2

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integral from 0 to pi of cos(3x)cos(3x)

\int_{0}^{π} cos (3 x) cos (3 x) d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{0}^{π} cos (3 x) cos (3 x) d x

Simplify

cos (3 x) cos (3 x) : cos^{2} (3 x)

= \int_{0}^{π} cos^{2} (3 x) d x

Rewrite using trig identities

= \int_{0}^{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_{0}^{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_{0}^{π} 1 d x + \int_{0}^{π} cos (6 x) d x)

\int_{0}^{π} 1 d x = π

\int_{0}^{π} cos (6 x) d x = 0

= \frac{1}{2} (π + 0)

Simplify

\frac{1}{2} (π + 0) : \frac{π}{2}

= \frac{π}{2}

\int \frac{2}{t ^{2} - 1} d t

\int \frac{- 2}{x ^{2} - 25} d x

\int sin (x) 2 + 3 cos (x) d x

y = (3 x^{2} + 2) (2 x - 5)

\frac{d}{d y} (\frac{y ^{4}}{8} + \frac{1}{4 y ^{2}})

What is the integral from 0 to pi of cos(3x)cos(3x) ?
The integral from 0 to pi of cos(3x)cos(3x) is pi/2