What is the integral from 0 to 2pi of 1+cos^2(x) ?

The integral from 0 to 2pi of 1+cos^2(x) is 3pi

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integral from 0 to 2pi of 1+cos^2(x)

\int_{0}^{2 π} 1 + cos^{2} (x) d x

3 π

Decimal

9.42477 \dots

Solution steps

\int_{0}^{2 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

= \int_{0}^{2 π} 1 d x + \int_{0}^{2 π} cos^{2} (x) d x

\int_{0}^{2 π} 1 d x = 2 π

\int_{0}^{2 π} cos^{2} (x) d x = π

= 2 π + π

Simplify

= 3 π

\int_{4}^{36} \frac{4}{x} d x

\int_{2}^{4} x^{2} - 6 x + 8 d x

\int_{- 1}^{2} 4 x - x^{2} d x

\int_{0}^{2} 3 x^{2} - 4 x + 2 d x

\int_{0}^{1} 2 π x (x^{2}) d x

What is the integral from 0 to 2pi of 1+cos^2(x) ?
The integral from 0 to 2pi of 1+cos^2(x) is 3pi