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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 = cos2x - sin2x
⇒ cos 2x = (1 - sin2x) - sin2x
⇒ cos 2x = 1 - 2sin2x
⇒ (1 - cos 2x)/2 = sin2x
Now, using the simplified value for sin2x, the integral converts to:
∫ sin2x dx = ∫ (1 - cos 2x)/2 dx
∫ sin2x = x/2 - (sin2x)/4 + c [Since the integral of cosax = sinax / a]
where, c is the constant of integration. For more information, click here.
Thus, the integral of sin2x is x/2 - (sin2x)/4 + c .