Integrating cos^2(x)+5sin^2(x)

Firstly, note that cos^2(x)+5sin^2(x)= cos^2(x) +sin^2(x) +4sin^2(x).

By trignoemtric identies, cos^2(x)+sin^2(x)=1 and so we can just integrate 1+4sin^2(x) since this is equal to cos^2(x)+5sin^2(x).

Again, by trignometric identities, 4sin^2(x)=4(1/2-1/2 cos(2x))=2-2cos(2x),

and so 1+4sin^2(x)=3-2cos(2x).

We can now integrate this much more easily...

3 integrates to 3x and -2cos(2x) integrates to -sin(2x).

Hence the integral, remembering the constant of integration, is...

3x -sin(2x) +c

RL
Answered by Rafe L. Maths tutor

7855 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Given x=Sqrt(3)sin(2t) and y=4cos^2(t), where 0<t<pi. Show that dy/dx = kSqrt(3)tan(2t).


1. A small stone is dropped from a height of 25 meters above the ground. i) Find the time taken for the stone to reach the ground ii) Find the speed of the stone as it reaches the ground


Integrate a^x with respect to x


How do you solve the integral of ln(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