MYTUTOR SUBJECT ANSWERS

354 views

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

Rafe L. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

1 year ago

Answered by Rafe, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

175 SUBJECT SPECIALISTS

£20 /hr

Samradnyee K.

Degree: Biomedical Engineering (Bachelors) - Kings, London University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I am a Biomedical Engineering student at King’s College London. Mathematics and Physics have always been my passion and I hope to pass on my love for the subjects to you through engaging and interactive sessions specially catered ...”

MyTutor guarantee

£20 /hr

George B.

Degree: Physics with Industrial experience (Masters) - Bristol University

Subjects offered: Maths, Physics

Maths
Physics

“Myself: I'm a Physics student at the University of Bristol. My passion is Physics and Maths. I think any theory can be made interesting and exciting. My tutorials will shows my informative and passionate nature.  I have numerous expe...”

£22 /hr

Alex B.

Degree: Physics (Masters) - Durham University

Subjects offered: Maths, Physics

Maths
Physics

“About me: I’m Alex and I have just completed my first year studying physics at Durham University, with a first. I have a passion for mathematics and how it can be applied to solve problems in physics. Throughout my A levels, other stu...”

About the author

Rafe L.

Currently unavailable: no new students

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“About Me: I am a maths student at the University of Warwick. From a young age I have always l been passionate about maths and I thoroughly enjoy teaching and helping others. I have volunteered as a football coach and as a maths tutor...”

MyTutor guarantee

You may also like...

Posts by Rafe

How to find the equation of a tangent to a curve at a specific point.

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

Other A Level Maths questions

Use the substition u = cos(x) to find the indefinite integral of -12sin(x)cos^3(x) dx

Prove that the d(tan(x))/dx is equal to sec^2(x).

Find dy/dx where y=e^(4xtanx)

How do I integrate cos^2(x)?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok