pls give the answer of this in integration
asked Jul 22, 2016 in Trigonometry Answers by nisarg

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

Let X=sin(2x)sin(4x)sin(6x)=sin(2x)sin(4x)(sin(4x)cos(2x)+cos(4x)sin(2x))=

sin(2x).2sin(2x)cos(2x)(2sin(2x)cos^2(2x)+(1-2sin^2(2x))sin(2x))=

2sin^2(2x)cos(2x)(2sin(2x)(1-sin^2(2x))+sin(2x)-2sin^3(2x))=

2sin^2(2x)(3sin(2x)-4sin^3(2x))cos(2x)=sin^3(2x)(3-4sin^2(2x)).2cos(2x)dx.

We want ∫Xdx.

Let p=sin(2x), dp=2cos(2x)dx.

∫Xdx=∫p^3(3-4p^2)dp=∫(3p^3-4p^5)dp=(3/4)p^4-(2/3)p^6.

That is: (3/4)sin^4(2x)-(2/3)sin^6(2x)+C where C=constant of integration.
answered Jul 22, 2016 by Rod Top Rated User (442,460 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
78,526 questions
82,365 answers
1,903 comments
63,405 users