MYTUTOR SUBJECT ANSWERS

329 views

How do you integrate by parts?

When you are faced with an integral which is a product, such as x.cos(x), you may be able to integrate it by parts. The statement of the integration by parts is that:

∫u(dv/dx)dx = uv-∫v(du/dx)dx

So if you have a function of the form u(dv/dx) (such as x.cos(x)​) it can be presented in the above form. In this case u = x and dv/dx = cos(x). 

When doing an intergration by parts it is useful to draw a grid first and work out what v and du/dx are (since we already know u and dv/dx) like so:

u = x

dv/dx = cos(x)

v = sin(x) (this is what you get when you integrate cos(x) as ∫(dv/dx)dx = v)

du/dx = 1 (what you get from differentiating u)

And so now that we have everything we need we can plug things into the equation:

∫x.cos(x)dx = uv-∫v(du/dx)dx = x.sin(x) - ∫1.sin(x)dx

and then to finish we integrate the last bit:

 ∫x.cos(x)dx = x.sin(x)+cos(x)+c (since this is an indefinite integral we must add a constant of integration c).

Timothy W. GCSE Maths tutor, A Level Maths tutor

1 year ago

Answered by Timothy, an A Level Maths tutor with MyTutor

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

184 SUBJECT SPECIALISTS

£20 /hr

Jake J.

Degree: Natural Sciences (Masters) - Durham University

Subjects offered: Maths, Further Mathematics + 1 more

Maths
Further Mathematics
-Personal Statements-

“About Me: My name's Jake, and I'm a Natural Sciences MSci student at Durham University! I'm an extremely patient, friendly person who believes that anyone can achieve incredible results. Having attained 10 A* grades at GCSE and A*A*A*...”

MyTutor guarantee

£20 /hr

Alicia E.

Degree: Classics BA (Bachelors) - Exeter University

Subjects offered: Maths, Latin+ 2 more

Maths
Latin
English Literature

“Hello! My name is Alicia, most people just call me Alice, I'm happy with either. I am studying Classics at the University of Exeter so I am very much committed to the classical world but still enjoy the subjects I took at A-Level and ...”

£20 /hr

Anahita G.

Degree: Maths and Economics (Bachelors) - York University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Economics
Chemistry
.TSA. Oxford.

“I am a maths and economics student at the University of York. I have always loved logical and analytical subjects, for example Maths and the Sciences. I also particularly enjoy economics as there are countless ways to analyse and conc...”

About the author

Timothy W.

Currently unavailable: until 01/10/2016

Degree: Mathematics (Bachelors) - Cardiff University

Subjects offered: Maths

Maths

“I am a mathematics student at Cardiff University and a friendly individual who is very patient. I have been teaching classical guitar for a year to a range of ages from 8 to 15 and so have experience as a teacher.”

You may also like...

Posts by Timothy

How do you differentiate parametric equations?

How do you factorise a quadratic equation?

How do you integrate by parts?

Other A Level Maths questions

How do you find an angle in a right-angled triangle when you are given two of its side's lengths?

The curve C has the equation y = 2x^2 -11x + 13. Find the equation of the tangent to C at the point P (2, -1).

Statistics: Dave throws a ball at a bucket. The probability the ball goes into the bucket is 0.4. Dave throws the ball four times. What is the probability that he gets it in twice?

What are the parameters of the Poisson distribution?

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