MYTUTOR SUBJECT ANSWERS

391 views

How do I do integration by parts?

Say we have an equation with the product of two subjects in the form f(x) = u(x)v(x).

Differentiating is simple, we would just multiply the differential* of u(x) by v(x) and add the differential of v(x) times by u(x). i.e f'(x) = u'(x)v(x)+v'(x)u(x).

Now, integrating is slight trickier. It can involve more than one step. We again have an equation of the product of two subjects. But this time, we write it as f(x) = u(x)v'(x). To find the integral we first need to differentiate u(x) and integrate v'(x). This will give us the following relevant terms (v'(x) is now not needed):

u(x)

u'(x)

v(x)

The integral is:

∫ f(x) dx = u(x)v(x) - ∫ v(x)u'(x) dx.

The last term which I have bolded and underlined is the term you need to reduce to a single subject of x e.g. x or x2 not xcos(x) to make it easily integratable. To do this, you need to choose which part is your u(x) and which your v'(x) These may take two of three times of repeating the same integration by parts but you should nomrally get there.

*Note: I am denoting differentials as f'(x), known as prime.

Doug A. GCSE Maths tutor, A Level Maths tutor

2 years ago

Answered by Doug, an A Level Maths tutor with MyTutor


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

262 SUBJECT SPECIALISTS

£24 /hr

Alex B.

Degree: Physics (Masters) - Durham University

Subjects offered: Maths, Physics

Maths
Physics

“About me: I’m Alex and I have just completed my first year studying physics at Durham University, with a first. I have a passion for mathematics and how it can be applied to solve problems in physics. Throughout my A levels, other stu...”

£20 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered: Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.MAT.

“About me: Hi I'm Ayyub, current student at Bristol university studying Maths with a masters. I'd like to think of myself as a very patient person when it comes to working with others and a generally friendly and approachable person, q...”

MyTutor guarantee

£20 /hr

Laura P.

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered: Maths

Maths

“As an Aerospace Engineering student in Bristol University, I am passionate about Mathematics and Science. Allow me to help you improve your grades, and hopefully inspire along the way!”

About the author

£20 /hr

Doug A.

Degree: Mathematics with Finance (Bachelors) - Leeds University

Subjects offered: Maths

Maths

“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

What does it mean to differentiate a function?

Below is a question from the Edexcel Maths Core 1 textbook, Solve the equation x^2 + 8x + 10 = 0 using completing the square.

If y = 5x^3 - 2x^2 + 2, what is dy/dx?

What is trigonometry? How do I remember sine, cosine and tangent?

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