Integrate the following between 0 and 1: (x + 2)^3 dx

Initially, we must recognise the simplest way to integrate this equation is using the 'reverse chain rule' method. 

This means raising the value of the power, in this case '3', by one, and then dividing by the new value of the power (which is four). This gives the integral to be 1/4 * (x + 2)^4 + c where c is a constant. We can check that this is correct by differentiating to give the original equation.

This is a definite integral, as there are bounds, so we must evaluate this new equation between 1 and 0: 

[1/4 * (x + 2)^4 + c] between 1 and 0 gives: 1/4[((1+2)^4 + c) - ((0 + 2)^4 + c)] = 1/4[81 - 16] = 16.25

Answered by Will E. Maths tutor

2423 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the simultaneous equations y = x^2 - 6x and 2y + x - 6 = 0


(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).


A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?


How to find the equation of a tangent to a curve at a specific point.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy