MYTUTOR SUBJECT ANSWERS

612 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

425 SUBJECT SPECIALISTS

£20 /hr

Harry C.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

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

MyTutor guarantee

£30 /hr

Laurie D.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“2nd year Maths student at Warwick, after a few tutorials you'll see Maths isn't the scary, hard subject most people think it is - it's actually really fun!”

£30 /hr

Joe C.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Joe, an experienced tutor and a University of Bristol graduate with a first class Degree in Mathematics.”

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

How would you integrate a function like f(x)=x(1-x)^6?

Solve the simultaneous equations y + 4x + 1 = 0 and y^2 + 5x^2 + 2x = 0

Show that the equation 5sin(x) = 1 + 2 [cos(x)]^2 can be written in the form 2[sin(x)]^2 + 5 sin(x)-3=0

How do I solve equations like 3sin^2(x) - 2cos(x) = 2

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