Find the antiderivative of (\sin x)^{2}

Adela Brown 2021-12-16 Answered
Find the antiderivative of (sinx)2
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Expert Answer

eskalopit
Answered 2021-12-17 Author has 31 answers
sin2xdx has no clear solutions.
Instead of integrating sin2x, you can integrate 12(1cos2x)
12(1cos2x)dx
=121cos2xdx
Now, use the sum rule to split this into:
121dx12cos2xdx
12x12cos2xdx
cos2xdx=12sin2x
So, we have 12x12cos2xdx
12x12(12sin2x)+C=12x14sin2x+C
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Wendy Boykin
Answered 2021-12-18 Author has 35 answers
(sin(x))2dx
sin2(x)dx
Rewrite using trig identities
1cos(2x)2dx
Take the constant out
=12×1cos(2x)dx
Apply the sum rule
=12(1dxcos(2x)dx)
As we know that 1dx=x, cos(2x)dx=12sin(2x), we have
=12(x12sin(2x))
=12(x12sin(2x))+C
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