What is the integral from-3 to 3 of cos^2((pix)/2) ?

The integral from-3 to 3 of cos^2((pix)/2) is 3

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integral from-3 to 3 of cos^2((pix)/2)

\int_{- 3}^{3} cos^{2} (\frac{π x}{2}) d x

3

Solution steps

\int_{- 3}^{3} cos^{2} (\frac{π x}{2}) d x

Rewrite using trig identities

= \int_{- 3}^{3} \frac{1}{2} (1 + cos (π 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_{- 3}^{3} 1 + cos (π 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_{- 3}^{3} 1 d x + \int_{- 3}^{3} cos (π x) d x)

\int_{- 3}^{3} 1 d x = 6

\int_{- 3}^{3} cos (π x) d x = 0

= \frac{1}{2} (6 + 0)

Simplify

\frac{1}{2} (6 + 0) : 3

= 3

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