Find the area between the curve y = 8 + 2x - x^2 and the line y = 8 - 2x.

First sketch the curve and the line, noting down where they intersect each axis.area under y = 8 + 2x - x2 is given by the integral between 0 and 4 of (8 + 2x - x2) dx.area under line is given by the integral between 0 and 4 of (8-2x) dx. It's easier to do this than using the formula for area of a triangle!!So total area:area = integral between 0 and 4 of (8 + 2x - x2) dx - integral between 0 and 4 of (8-2x) dxarea = integral between 0 and 4 of (8 + 2x - x2 - (8-2x))dx Note we can combine the two integrals!!area = integral between 0 and 4 of (4x - x2) dxarea = [2x2 - x3/3]40 = 32/3

Answered by Maths tutor

4254 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do you simplify something of the form Acos(x) + Bsin(x) ?


Why does sin^2(x)+cos^2(x)=1?


Question 3 on the OCR MEI C3 June 2015 paper. Find the exact value of Integral x^3 ln x dx between 1 and 2.


differentiate with respect to x : y = x^2 -5x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning