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...

11 months ago

Answered by Olaoluwa, an A Level Maths tutor with MyTutor

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


Nick B. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor
£20 /hr

Nick B.

Degree: Computer Science (Masters) - Bristol University

Subjects offered:Maths, Physics


“About me: I am currently studying computer science at the University of Bristol after taking quite a varied set of subjects at A Level. I have always enjoyed helping others when it comes to school. Since I came to university I have bee...”

£20 /hr

Ruadhan P.

Degree: Physics (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

-Personal Statements-

“I am a currently studying Physics at the University of Nottingham. The way Physics and Maths are able to explain the Universe around us truly fascinates me and I hope to be able to share that fascination and excitement for the subject...”

£20 /hr

Liam O.

Degree: Economics (Bachelors) - Cardiff University

Subjects offered:Maths


“About me: My name is Liam, I study Economics at Cardiff business school. I have always thought of myself as a patient, understanding person who is always keen for the opportunity to help others. I have previously tutored reading at pr...”

MyTutor guarantee

About the author

Olaoluwa O.

Currently unavailable: for new students

Degree: Natural Sciences (Bachelors) - Durham University

Subjects offered:Maths, Latin+ 1 more

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

how to find flight time/distance and greatest hight of projectiles?

How do you find the equation of a tangent to a curve at a particular point?

Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.

If y = 2^x, solve the equation 8(4^x) + 9(2^x) + 1 = 0 in terms of y.

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