+91-705-589-3577
FlagBACK
Flag Integral Calculus> Integrate the following ...........,,.......
question mark

Integrate the following ...........,,....,: sin4x.cos3x.sin2x

Ritz , 8 Years ago
Grade 12
anser 1 Answers
Arun
Note that sin(A)sin(B) = (1/2) [cos(A - B) - cos(A + B)]. 
Also, cos(-A) = cos(A). 

Therefore, 
sin(2x)sin(4x) = (1/2) [cos(2x) - cos(6x)]. 

Also note that cos(A)cos(B) = (1/2) [cos(A + B) + cos(A - B)]. 

∫sin(2x)cos(3x)sin(4x) dx 
= ∫ (1/2) [cos(2x) - cos(6x)] cos(3x) dx 
= (1/2) ∫ [cos(2x)cos(3x) - cos(6x)cos(3x)] dx 
= (1/2)(1/2) ∫ [cos(5x) + cos(x) - cos(9x) - cos(3x)] dx 
= (1/4) ∫[cos(x) - cos(3x) + cos(5x) - cos(9x)] dx 
= (1/4) [ sin(x) - sin(3x)/3 + sin(5x)/5 - sin(9x)/9 ]
 
 
Regards
Arun (askIITians forum expert)
ApprovedApproved
Last Activity: 8 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Other Related Questions on integral calculus

question mark
The area of a square field is 640000cm2.what is its area in hectares
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Please solve this integration. I am facing difficulty in it
 How to solve this. Please solve anyone. Humble request
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
Using laplace transform, solve d2y/dt2 + dy/dt = t2 +2t given that y=4 and y’=-2 and t=0
integral calculus
1 Answer Available

Last Activity: 3 Years ago

question mark
If 4th term of an A.p is zero, show that the 8th term is double the 6th term
 
integral calculus
1 Answer Available

Last Activity: 4 Years ago