How to integrate sin2x?
Integration is an inverse process of differentiation. Let's use the concept of integration to solve the problem.
Answer: The integral of sin2x is x/2 - (sin2x)/4 + c .
Go through the explanation to understand better.
To solve: ∫ sin2x
Let us first simplify sin2x, using the trigonometric identity
cos 2x = sin2x - cos2x
⇒ cos 2x = sin2x - (1 - sin2x)
⇒ cos 2x = 2sin2x - 1
⇒ (cos 2x + 1)/2 = sin2x
Now, using the simplified value for sin2x, the integral converts to:
∫ sin2x = ∫ (cos 2x + 1)/2
∫ sin2x = x/2 - (sin2x)/4 + c [Since the integral of cosax = - sinax / a]
where, c is the constant of integration