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

The integral from-2pi to 2pi of sin^2(x)+1 is 6pi

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integral from-2pi to 2pi of sin^2(x)+1

\int_{- 2 π}^{2 π} sin^{2} (x) + 1 d x

6 π

Decimal Notation

18.84955 \dots

Solution steps

\int_{- 2 π}^{2 π} sin^{2} (x) + 1 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_{- 2 π}^{2 π} sin^{2} (x) d x + \int_{- 2 π}^{2 π} 1 d x

\int_{- 2 π}^{2 π} sin^{2} (x) d x = 2 π

\int_{- 2 π}^{2 π} 1 d x = 4 π

= 2 π + 4 π

Simplify

= 6 π

\int_{1}^{2} - \frac{5 ln ( x )}{x ^{2}} d x

\int \frac{- 5}{x} d x

\int x^{- 6} (x + 1) d x

y^{^{''}} - 9 y^{^{'}} + 18 y = 2 sin (5 t)

e^{c o s (s i n (x^{2}))}

What is the integral from-2pi to 2pi of sin^2(x)+1 ?
The integral from-2pi to 2pi of sin^2(x)+1 is 6pi