How do you integrate sin(3x)cos(5x)?

STEP 1 Cannot integrate directly in this form, therefore use a trigonometric identity. Identity: sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2) STEP 2 (A+B)/2 = 3x             A + B = 6x   (1) (A-B)/2 = 5x              A - B = 10x     (2) STEP 3 Solve simultaneous equations (1) and (2) (1) + (2)      2A = 16x    A = 8x Substitute A into (1)      B = -2x STEP 4 Substitute values for A and B into the trigonometric identity. sin(3x)cos(5x) = (1/2)(sin(8x) + sin(-2x)) STEP 5 Now integrate. {Note: integral of sine is negative cosine} = (1/2)(integral sign)[sin(6x) + sin(-2x)] dx = (1/2)[(1/8)(-cos(8x)) + (1/2)cos(-2x)] + C = (-1/16)cos(8x) + (1/4)cos(-2x) + C //

CF
Answered by Catherine F. Maths tutor

7098 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

I did all the past papers but I still only achieved a C grade, what am I doing wrong?


The gradient of the curve at point (x,y) is given by dy/dx = [7 sqrt(x^5)] -4. where x>0. Find the equation of the curve given that the curve passes through the point 1,3.


Two points have coordinates (1,-6) and (-2,3). Find the equation of the line which joins them, and their midpoint.


The second and fifth terms of a geometric series are 750 and -6 respectively. Find: (1) the common ratio; (2) the first term of the series; (3) the sum to infinity of the series


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