SOLUTION: What is the integral of a trigonometric function squared? for example,. sin(squared) of 3x.

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Question 30631: What is the integral of a trigonometric function squared? for example,. sin(squared) of 3x.
Answer by venugopalramana(3286) About Me  (Show Source):
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What is the integral of a trigonometric function squared? for example,. sin(squared) of 3x.
IT DEPENDS ON THE FUNCTION..
FOR EXAMPLE
INTEGRAL {SEC (X)}^2 IS TAN(X)+K
BUT IF YOU WANT FOR
{SIN(3X)}^2....WE FIRST CHANGE IT TO MULTIPLE ANGLE BY USING
COS(2X) =1-2*{SIN(X)}^2....FORMULA...SO WE GET
{SIN(3X)}^2 = {1-COS(2*3X)}/2=(1-COS(6X))/2...NOW INTEGRATION IS EASY ..IT IS
={X-SIN(6X)/6}/2 =X/2 - (1/12)*SIN(6X)