I'm a bit confused as to why I need to add 1/4 and 4 to the integral and get (2sinxcosx)^2. Why can't I just sqrt the original integral instead and evaluate from (sinxcosx)^2 instead?
#Calculus II: Trigonometric Integral
vapid swift
wise epochBOT
I'm a bit confused as to why I need to add 1/4 and 4 to the integral and get (2s...
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patent cloud
I'm a bit confused as to why I need to add 1/4 and 4 to the integral and get (2s...
there may be multiple ways of doing 1 integral, but how would you integrate (sinxcosx)^2
vapid swift
there may be multiple ways of doing 1 integral, but how would you integrate (sin...
I did:
∫sin(x)^2 cos(x)^2 dx
∫ [sin(x)cos(x) ]^2 dx
∫ (1/2)sin(2x) dx
vapid swift
Yes, I understand, but I don't understand how to get 1/4 and 4. I see that it was added in to make it form correctly, but I don't understand why and the choosing of it. I don't understand the rule of adding 1/4 and 4 into the integral.
patent cloud
you need to multiply by 1 to make the integral not change, and they just wanted 4sin^2(x)cos^2(x)
to get sin^2(2x)
so you need to also insert a 1/4 to balance it
vapid swift
Ohhhhh. Thank you so much! You are a life saver! Thank you, thank you!
Would that work with any number like 1/16 and 16, or would it need to be exactly 1/4 and 4??
patent cloud
you can insert any inverse pair (except 0 ofc)