Express cos2x in the form a*cos^2(x) + b and hence show that the integral of cos^2(x) between 0 and pi/2 is equal to pi/a.

Apply the double angle formula to cos2x to yield the requested result.
cos2x = 2cos^2(x) - 1
Spot that the question asks us to prove the value of cos^2(x) when integrated, and that we can move the variables in the above equation to have cos^2(x) on its own.
cos^2(x) = (1/2)*(cos2x +1)
Now we can integrate the the equation between 0 and pi, and we should get the right hand side equal to pi/4.
[ (1/4)*sin2x + x/2 ] from 0 to pi/2
substituting pi/2 into the above equation gives pi/4. Substituting 0 into the above equation gives 0.
So we get pi/4 - 0 = pi/4

LP
Answered by Louis P. Maths tutor

4541 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

differentiate (1+2x^2)^(1/2)


a) i) find dy/dx of y = 3x^4 - 8x^3 - 3 ii) then find d^2y/dx^2 b) verify that x=2 at a stationary point on the curve c c) is this point a minima or a maxima


How do I integrate ∫ xcos^2(x) dx ?


The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the


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