How do I integrate Cos x Sin x dx?
How do I integrate Cos x Sin x dx? I'm working on an engineering problem and having trouble getting up to speed with simple integral calculus. Any help is much appreciated!
How do I integrate Cos x Sin x dx? I'm working on an engineering problem and having trouble getting up to speed with simple integral calculus. Any help is much appreciated!
Sridhar R
Favorite Answer
you can solve in different ways you will get diff answer but they will be right
1) put sinx = t
cosxdx = dt
∫ tdt = t^2/2 +c = 1/2sin^2 X +c
2) sinxcosx = 1/2 sin2x
∫ 1/2sin2x dx = -1/4 cos2x +c
Anonymous
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There are different ways to solve this, but here's the way I'd go about it: ∫ sin(x) / cos^3 (x) dx = ∫ sin(x) [ cos (x) ]^-3 dx = (-1/2) ∫ sin(x) * -2[ cos (x) ]^-3 dx = (1/2) ∫ -sin(x) * -2[ cos (x) ]^-3 dx = (1/2) cos^-2 (x) + c If you use "u substitition" by letting u = cos(x) so that du = -sin(x) dx, etc. you'll get the right answer. I just noticed that you have cos(x) raised to some power, and that the derivative of cosine is -sin(x), so I did the "chain rule" in reverse. Somebody else answered (1/2)tan²(x) + c, which is not wrong. If you use the fact that sin^2 (x) + cos^2(x) = 1, and apply it to the other answer, then you have: (1/2) (1/cos^2 (x)) + c = (1/2) [sin^2 (x) + cos^2(x)]/cos^2 (x)) + c = (1/2) [tan^2 (x) + 1] + c = (1/2)tan^2 (x) + 1/2 + c = (1/2)tan^2 (x) + (1/2 + c) = (1/2)tan^2 (x) + (a constant)
Anonymous
Integrate Sinxcosx
Anonymous
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How do I integrate Cos x Sin x dx?
How do I integrate Cos x Sin x dx? I'm working on an engineering problem and having trouble getting up to speed with simple integral calculus. Any help is much appreciated!
horth
Integral Of Cosxsinx