What is the integral of sin(x)*sin(2-x) ?

The integral of sin(x)*sin(2-x) is 1/2 (-cos(2)x+1/2 sin(2x-2))+C

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integral of sin(x)*sin(2-x)

\int sin (x) \cdot sin (2 - x) d x

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

Solution steps

\int sin (x) sin (2 - x) d x

Rewrite using trig identities

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

Take the constant out:

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

= \frac{1}{2} \cdot \int - cos (2) + cos (2 x - 2) 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

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

\int cos (2) d x = cos (2) x

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

= \frac{1}{2} (- cos (2) x + \frac{1}{2} sin (2 x - 2))

Add a constant to the solution

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

What is the integral of sin(x)*sin(2-x) ?
The integral of sin(x)*sin(2-x) is 1/2 (-cos(2)x+1/2 sin(2x-2))+C