Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers


781,677 users

Enter a quick description of your question...trigonometric integrals

+2 votes
What is the integral of sin^3 x cos^3 x dx
asked Dec 25, 2012 in CALCULUS by skylar Apprentice

1 Answer

+2 votes
∫sin^3xcos^3x dx

Rewrite cos^3x=cos^2x*cosx

∫sin^3xcos^2x*cosx dx

using trignometrical formula sin^2x+cos^2x=1

∫sin^3x(1-sin^2x) cosx dx

∫(sin^3x-sin^5x) cosx dx

∫sin^3xcosx dx-∫sin^5x cosx dx

let t=sinx then


dt=cosx dx

Rewrite the integral by substituting t=sinx and dt=cosx dx

∫t^3 dt-∫t^5 dt

t^4/4 -t^6/6

Substitute t = sinx then


The integral of sin^3xcos^3x dx is Sin^4x/4-Sin^6x/6
answered Dec 25, 2012 by sachin Rookie

Related questions

asked Jul 10, 2014 in CALCULUS by anonymous