Integrate cos(4x)sin(x)

MYTUTOR SUBJECT ANSWERS

Answers / Further Mathematics / A Level / Integrate cos(4x)sin(x)

1593 views

Integrate cos(4x)sin(x)

The easiest way of approaching this question is to use De Moivre's formula:

e^(inx) = cos(nx) + isin(nx)

from which it is simple to show that cos(nx) = (e^(inx) + e^(-inx)) / 2 and sin(nx) = (e^(inx))- e^(-inx)) /2i

therefore, cos(4x)sin(x) = (e^(4ix) + e^(-4ix)) * ((e^(ix)) - (e^(-ix)) / 4i

= [e^(5ix) - e^(-5ix) - e^(3ix) + e^(-3ix)] / 4i

= sin(5x)/2 - sin(3x)/2

Finally, integrating, this gives cos(3x)/6 - cos(5x)/10 + integration constant

This can also be done by using various trigonometric identities, however this method is simpler and can continue to be applied to more complex questions.

Kirill M. A Level Maths tutor, A Level Further Mathematics tutor, A ...

2 years ago

Answered by Kirill, an A Level Further Mathematics tutor with MyTutor

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

147 SUBJECT SPECIALISTS

Harry C. IB Further Mathematics tutor, A Level Further Mathematics ...

View profile

£20 /hr

Harry C.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Further Mathematics , Physics+ 1 more

“Second year Engineering student, I'm passionate, dedicated and personable. A- Level Maths and Physics (A*AA).”

MyTutor guarantee

Save profile

Vlad B. 13 Plus Maths tutor, 11 Plus Maths tutor, GCSE Maths tutor, ...

View profile

£20 /hr

Vlad B.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Further Mathematics , Maths

“Hi! I am studying Mathematics at Bath University and I am passionate about teaching, and learning mathematics.”

MyTutor guarantee

| 1 completed tutorial

Save profile

Ryan A. IB Maths tutor, A Level Maths tutor, GCSE Maths tutor, IB Fur...

View profile

£20 /hr

Ryan A.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Maths+ 1 more

“Passionate about passing down a greater understanding of maths and instilling confidence in all students.”

5.0

6 reviews | 9 completed tutorials

Save profile

See more A Level Further Mathematics tutors

About the author

View profile

£24 /hr

Kirill M.

Degree: Physics (Masters) - Oxford, St Catherine's College University

Subjects offered:Further Mathematics , Physics+ 2 more

“Me Hi, I'm Kirill, I'm a 3rd year physicist at Oxford. Whether you are looking for exam preparation or for a better understanding of the material that you are covering in your studies of Maths or Physics, I can help you reach your goa...”

5.0

9 reviews | 57 completed tutorials

Save profile

Version:	3.49.8
Build:	44de53c98908
Time:	2017-09-14T10:02:09Z

MYTUTOR SUBJECT ANSWERS

Integrate cos(4x)sin(x)

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

147 SUBJECT SPECIALISTS

About the author

You may also like...

Posts by Kirill

Other A Level Further Mathematics questions

One-to-one help is at your fingertips