Integrate cos(4x)sin(x)

The easiest way of approaching this question is to use De Moivre's formula: e^(inx) = cos(nx) + isin(nx) from which it is simple to show that cos(nx) = (e^(inx) + e^(-inx)) / 2 and sin(nx) = (e^(inx))- e^(-inx)) /2i therefore, cos(4x)sin(x) = (e^(4ix) + e^(-4ix)) * ((e^(ix)) - (e^(-ix)) / 4i= [e^(5ix) - e^(-5ix) - e^(3ix) + e^(-3ix)] / 4i= sin(5x)/2 - sin(3x)/2Finally, integrating, this gives cos(3x)/6 - cos(5x)/10 + integration constantThis can also be done by using various trigonometric identities, however this method is simpler and can continue to be applied to more complex questions. 

KM
Answered by Kirill M. Further Mathematics tutor

13681 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Unfortunately this box is to small to contain the question so please see the first paragraph of the answer box for the question.


Find a vector that is normal to lines L1 and L2 and passes through their common point of intersection where L1 is the line r = (3,1,1) + u(1,-2,-1) and L2 is the line r = (0,-2,3) + v(-5,1,4) where u and v are scalar values.


What are the conditions required for the poisson distribution?


How do you prove the formula for the sum of n terms of an arithmetic progression?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences