MYTUTOR SUBJECT ANSWERS

694 views

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

For a question like this, it would be far too time-consuming to expand the bracket and then multiply through by x. It might then seem that integration by parts is the optimal solution, but this is actually not necessary.

If you make the substitution u=1-x then you have du=-dx. Then the integral of x(1-x)^6 with respect to x is equivalent to the integral of -(1-u)u^6 with respect to u. By multiplying through, we have u^7-u^6 which is not difficult to integrate.

An important thing to remember in this is always to remember to find dx in terms of du - do not assume that dx=du because it rarely does. Finally, make sure you sub x back into your final answer.

If you are given a definite integral where you need a substitution, always remember to change your limits appropriately. There is then no need to sub into your integral at any point in the working

Olaoluwa O. GCSE Further Mathematics  tutor, A Level Further Mathemat...

1 year ago

Answered by Olaoluwa, an A Level Maths tutor with MyTutor


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

346 SUBJECT SPECIALISTS

£26 /hr

Ben J.

Degree: Physics and Computer Science (Natural Sciences) (Masters) - Durham University

Subjects offered:Maths, Science+ 6 more

Maths
Science
Physics
Further Mathematics
Computing
Chemistry
Biology
-Personal Statements-

“About Me: I'm a Physics and Computer Science student at Durham University, which sounds boring but it's actually really fun.I've got a great knack for making boring things more exciting, which is a good job given my degree title!  I'...”

£26 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best!”

£24 /hr

Hinsum W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi, I'm a first year medic at Edinburgh. I've had 7 years' worth of experience teaching children Maths and English and have mentored lower school peers, so I'm bound to have an approach that will suit your learning style!”

About the author

Olaoluwa O.

Currently unavailable: for new students

Degree: Natural Sciences (Bachelors) - Durham University

Subjects offered:Maths, Latin+ 1 more

Maths
Latin
Further Mathematics

“About me I am a 19 year old Mathematics & Philosophy student at Durham University. I am particularly interested in the analytic side of pure mathematics as well as Latin language, two subjects which I enjoyed studying through to A lev...”

You may also like...

Posts by Olaoluwa

How do I know which method of integration to use?

How do you translate long, complex Latin sentences?

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

Other A Level Maths questions

If y = (1+3x)^2, what is dy/dx?

Outline the various ways that you can differentiate a function

What actually are sin, cos and tan?

How do I invert a 2x2 square matrix?

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