What is the integral of sin^2(t ?

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

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integral of sin^2(t

\int sin^{2} (d) t

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

Solution steps

\int sin^{2} (d) t dd

Take the constant out:

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

= t \cdot \int sin^{2} (d) dd

Rewrite using trig identities

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

Take the constant out:

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

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 dd = d

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

= t \frac{1}{2} (d - \frac{1}{2} sin (2 d))

Add a constant to the solution

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

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