Integrate sin2x dx

We have to integrate of sin2x

Solution

For sin2(X), we will use the cos double angle formula:

cos(2X) = 1 – 2sin2(X)

The above formula can be rearranged to make sin2(X) the subject:

sin2(X) = 1/2(1 – cos(2X))

No we can rewrite it as

∫sin2(X)dX = ∫1/2(1 – cos(2X))dX

Because 1/2 is a constant, we can remove it from the integration to make the calculation simpler. We are now integrating:

1/2 x ∫(1 – cos(2X)) dX = 1/2 x (X – 1/2sin(2X)) + C

Simplifying the above equation gives us a final answer:

∫sin2(X) dX = 1/2X – 1/4sin(2X) + C

Answer

∫sin2(X) dX = 1/2X – 1/4sin(2X) + C

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