What is the integral from-6pi to pi of cos^2(x) ?

The integral from-6pi to pi of cos^2(x) is (7pi)/2

Popular >

integral from-6pi to pi of cos^2(x)

\int_{- 6 π}^{π} cos^{2} (x) d x

\frac{7 π}{2}

Decimal

10.99557 \dots

Solution steps

\int_{- 6 π}^{π} cos^{2} (x) d x

Rewrite using trig identities

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

\int_{- 6 π}^{π} 1 d x = 7 π

\int_{- 6 π}^{π} cos (2 x) d x = 0

= \frac{1}{2} (7 π + 0)

Simplify

\frac{1}{2} (7 π + 0) : \frac{7 π}{2}

= \frac{7 π}{2}

\int_{4}^{5} \frac{1}{25 - x ^{2}} d x

\int_{2}^{3} x ln (x) d x

\int_{0}^{5} \frac{t}{11 + t ^{2}} d t

\int_{1}^{2} 2^{3 x} d x

\int_{0}^{2 \cdot π} cos^{2} (x) d x

What is the integral from-6pi to pi of cos^2(x) ?
The integral from-6pi to pi of cos^2(x) is (7pi)/2