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

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

Popular >

integral of sin^2(t)

integral

sin^{2} (t)

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

Solution steps

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

Rewrite using trig identities

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

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 t) d t

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

\int 1 d t = t

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

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

Add a constant to the solution

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

\int 8 x^{7} e^{8 x^{8}} d x

\int \frac{x - 2}{( x - 1 ) ( x ^{2} - 2 x + 5 )} d x

\int \frac{x}{( x + 2 ) ^{\frac{1}{4}}} d x

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

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