Use the substitution u = cos 2x to find ∫(cos^2*(2x) *sin3 (2x)) dx

∫(cos2 2x *sin3 2x)dx u = cos2x - u =(du/dx) = -2sin2x - differentiate u dx = du/(-2sin(2x)) - dx = -1/2 ∫cos22x * sin22x du - sub in dx-1/2 ∫u2(1-u2)du - put in terms if u -1/2 [ u3/3 - u5/5 ] + c - integrate in terms of u (cos52x)/10 - (cos32x)/6 - Final answer





WB
Answered by Will B. Maths tutor

7294 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has equations: x=2sin(t) and y=1-cos(2t). Find dy/dx at the point where t=pi/6


What is the moment about the pivot C


Find the intersection points between the graphs y=2x+5 and y=x^2-9.


a)Given that 10 cosec^2(x) = 16 - 11 cot(x) , find the possible values of tan x .


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences