Find ∫sin4x dx.

∫ sin4x dx = ∫ (sin2x)2 dx
= ∫ [(1 − cos 2x)/2]2 dx
= (1/4) ∫ (1 − cos 2x)2 dx
= (1/4) ∫ (1 − 2 cos 2x + cos22x) dx
= (1/4) ∫ [1 – 2 cos 2x + {(1 + cos 4x)/2 }] dx
= (1/4) ∫ dx – (2/4) ∫ cos 2x dx + (1/8) ∫ (1 + cos 4x) dx
= (x/4) – (1/2) [(sin 2x)/2] + (x/8) + (1/8) [(sin 4x)/4] + C
= (3/8)x + (1/32) sin(4x) − (1/4) sin(2x) + C

Was this answer helpful?

 
   

0 (0)

(0)
(0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

BOOK

Free Class

Ask
Question