MYTUTOR SUBJECT ANSWERS

474 views

How do you integrate by parts?

This is one of the trickiest methods of calculus on the course, but it's important to know, and is very doable if you set up the problem right and remember the steps. 

Integration by parts works when you have to integrate a function of the type f=u(dv/dx). All you have to remember is that, and the formula(dv/dx) dx = uv - ∫ (du/dx) dx

Ok, let's try an example. 

Say you're asked to integrate xsin(x). 

I find it makes it easiest to write out all the things I need for the formula before I plug them in. 

We'll choose x to be u, because differentiating x makes it more simple, while differentiating sin(x) doesn't really help that much. You always choose u to be the part that comes out simplest when differentiated.

So:                                                            u = x

Then, by differentiating,                du/d= 1

and also:                                               dv/dx = sin(x)

Then, integrating to find v,             v = -cos(x). 

Now, all we have to do is plug that back into the formula from earlier:

             ∫ xsin(x) dx = -xcos(x) - ∫ -cos(x) (1) dx.

Which is way easier! Integrating cos(x) gives sin(x) + c (always remember c!), so we end up with

             ∫ xsin(x) dx = -xcos(x) + sin(x) + c.

And that's your answer!

Isaac E. GCSE Physics tutor, A Level Physics tutor, GCSE Maths tutor,...

1 year ago

Answered by Isaac, who has applied to tutor A Level Maths with MyTutor


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

269 SUBJECT SPECIALISTS

£22 /hr

Kashf S.

Degree: Chemistry (Bachelors) - University College London University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Hi, I'm a first year Chemistry student at UCL, I have experience in tutoring and am willing to tutor people of all abilities”

£20 /hr

Madeleine N.

Degree: Maths and Physics (Masters) - Durham University

Subjects offered:Maths, Spanish+ 2 more

Maths
Spanish
Physics
Further Mathematics

“Enthusiastic student, studying Maths and Physics at Durham university: keen to work hard with students to improve their results.”

William S. 11 Plus Maths tutor, A Level Maths tutor, 13 plus  Maths t...
£20 /hr

William S.

Degree: Medicine (Other) - St. Andrews University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“I am a medical student at the university of St Andrews. I have always loved maths and sciences, and hope to share that passion with you too! I am patient and very friendly, so hopefully you will enjoy our sessions. Of course, you will...”

About the author

£20 /hr

Isaac E.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics

Maths
Physics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Question 3 on the OCR MEI C1 June 2015 paper. Evaluate the following. (i) 200^0 (ii) (9/25)^(-1/2)

The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

Integrate ln(x) by parts then differentiate to prove the result is correct

How do you differentiate parametric equations?

View A Level Maths tutors

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

mtw:mercury1:status:ok