586 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

2 years ago

Answered by Rafe, an A Level Maths tutor with MyTutor

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

#### 306 SUBJECT SPECIALISTS

£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my years of experience tutoring, we will be able to surpass the grades you want!”

£24 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.MAT.

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

£24 /hr

Ed W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Further Mathematics + 3 more

Maths
Further Mathematics
Chemistry
Biology
-Medical School Preparation-

“Hi! I'm Ed and I'm currently studying Medicine at the University of Edinburgh. I tutor at GCSE and A Level forBiology, Chemistry and Maths, and at GCSE level forFurther Maths. These are subjects I'm very comfortable in and enjoy. With ...”

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

Differentiate y=x(e^x)

I'm supposed to calculate the differential of f(x)= sin(x)*ln(x)*(x-4)^2 using the product rule. I know what the product rule is but I can't split this into two bits that are easy to differentiate. How do I do it?

The Curve, C, has equation: x^2 - 3xy - 4y^2 +64 =0 Find dy/dx in terms of x and y. [Taken from Edexcel C4 2015 Q6a]

How do you find the gradient of a line at a certain point when f(x) is in the form of a fraction, where both the numerator and denominator are functions of x?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.