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Question

What is integral of sin2x?


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Solution

Step 1: Substitute u in the place 2x in the given integration

Let I=sin2xdx ….(1)

and 2x=u

Now differentiate the equation 2x=u with respect to x

2dx=du

dx=12du

Now putting dx=12duin equation (1)

I=12sinudu

Step 2: Apply the formula sinxdx=-cosx+c

I=12sinudu

I=-12cosu+c … where c is an integration constant

Putting u=2x

I=-12cos2x+c

Hence the integral of cos2x is -12cos2x+c, where c is an integration constant.


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