How do I find the area bounded by the curve y=-x^2+4 and the line y=-x+2?

First sketch the line and the curve on the same axes (I would show this using the whiteboard).Then we want to find the points of intersection so set the two equations equal to each other and rearrange to get the equation x^2-x-2=0. If we solve this for x and substitute the values of x back into one of the equations we find that the points of intersection are at (-1,3) and (2,0). Then to find the area under the curve we can integrate -x2+4 between x=-1 and x=2 to get 9 units squared. But this is not the area we want as it includes the area under the line. So we need to subtract the area under the line between x=-1 and x=2. From the sketch this is the same as subtracting the area of the triangle with vertices at (-1,3),(-1,0) and (2,0) which equals 9/2. So the final solution is 9-9/2 = 9/2 units squared.

SH
Answered by Sarah H. Maths tutor

2852 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is the point of differentiation?


Use simultaneous equations to find the points where the following lines cross: 3x - y = 4 and x^2 + 7y = 5


Find the factors of x^3−7x−6


At each point P of a curve for which x > 0 the tangent cuts the y-axis at T, and N is the foot of the perpendicular from P to the y-axis. If T is always 1 unit below N and the curve passes through the point (1,0), find the Cartesian equation of the curve.


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 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences