What is the integral of (sin(θ))^2 ?

The integral of (sin(θ))^2 is 1/2 (θ-1/2 sin(2θ))+C

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integral of (sin(θ))^2

\int (sin (θ))^{2} d θ

\frac{1}{2} (θ - \frac{1}{2} sin (2 θ)) + C

Solution steps

\int (sin (θ))^{2} d θ

Simplify

= \int sin^{2} (θ) d θ

Rewrite using trig identities

= \int \frac{1 - cos ( 2 θ )}{2} d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 - cos (2 θ) d θ

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 1 d θ - \int cos (2 θ) d θ)

\int 1 d θ = θ

\int cos (2 θ) d θ = \frac{1}{2} sin (2 θ)

= \frac{1}{2} (θ - \frac{1}{2} sin (2 θ))

Add a constant to the solution

= \frac{1}{2} (θ - \frac{1}{2} sin (2 θ)) + C

\frac{d}{d x} (2 x^{5} - e^{x})

\int x^{5} ln (x) d x

\int \frac{x ^{2}}{( 81 - x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{x - 2}{x ^{3} - 3 x ^{2} - x + 3} d x

\frac{d P}{d t} = 0.2 P (1 - \frac{P}{1000}) - 32

What is the integral of (sin(θ))^2 ?
The integral of (sin(θ))^2 is 1/2 (θ-1/2 sin(2θ))+C