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Difficult integration

by ookt2c
Tags: difficult, integration
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Feb6-08, 05:38 PM
P: 16
integrate sin^4(2x) without using the reduction stuck.
im pretty sure you have to use integration by parts.
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Feb6-08, 06:05 PM
P: 64
Try using double-angle formulae a couple of times.
Feb6-08, 06:09 PM
HW Helper
P: 6,202
The double angle formula for cos will help I believe.

Feb7-08, 03:53 AM
P: 230
Difficult integration

don't know what the reduction formula is, maybe it is the trick i'm about to give you

[tex] \int sin(2x)^4 dx = \frac{1}{2} \int sin(u)^4 du = \frac{1}{2} \int (sin(u)^2)^{3/2} sin(u) du = \frac{1}{2} \int (1-cos(u)^2)^{3/2} sin(u)du = \frac{1}{2} \int (1-t^2)^{3/2} dt = \int sqrt((1-t^2)^3) [/tex]

maybe you can do this???, of cause you have to keep track of all the substitutions to get how sin and y are related but that should be possible.
Feb7-08, 10:38 AM
P: 1,633
This thread is already somewhere else. I mean the exact same question.

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