What is the integral from 0 to pi/2 of 64cos^4(x)-4 ?

The integral from 0 to pi/2 of 64cos^4(x)-4 is 10pi

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integral from 0 to pi/2 of 64cos^4(x)-4

\int_{0}^{\frac{π}{2}} 64 cos^{4} (x) - 4 d x

10 π

Decimal Notation

31.41592 \dots

Solution steps

\int_{0}^{\frac{π}{2}} 64 cos^{4} (x) - 4 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

= \int_{0}^{\frac{π}{2}} 64 cos^{4} (x) d x - \int_{0}^{\frac{π}{2}} 4 d x

\int_{0}^{\frac{π}{2}} 64 cos^{4} (x) d x = 12 π

\int_{0}^{\frac{π}{2}} 4 d x = 2 π

= 12 π - 2 π

Simplify

= 10 π

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What is the integral from 0 to pi/2 of 64cos^4(x)-4 ?
The integral from 0 to pi/2 of 64cos^4(x)-4 is 10pi