What is the integral of sin^2(o) ?

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

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integral of sin^2(o)

\int sin^{2} (o) d o

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

Solution steps

\int sin^{2} (o) d o

Rewrite using trig identities

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

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 o) d o

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 o - \int cos (2 o) d o)

\int 1 d o = o

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

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

Add a constant to the solution

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

\frac{( s + 3 ) ^{2}}{s ( s ^{2} + 10 )}

\int 1 x^{2} d x

\frac{d}{d x} (15 x^{2})

\int \frac{( x - 1 ) ^{2}}{x} d x

\int_{0}^{1} \frac{89}{x ^{5}} d x

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