Find the area between the positive x axis and the line given by y=-(x^2)+2x

The first piece of understanding needed to answer this question is that integration can be used to find the area under a graph between two points. However, before we can integrate we must find the bounds between which we should integrate. With the aid of a graph we can see that those bounds are the two roots of the quadratic. By factorizing we can show that they are x=0 and x=2. Now we integrate:-x2+2x between the bounds x=0 and x=2, with respect to x. This gives us the final answer of 4/3.

Related Maths A Level answers

All answers ▸

Integration by parts: Integrate the expression x.ln(x) between 1 and 2.


What is the indefinite integral of (x^4)*(-sin(x)) dx


The straight line with equation y=3x-7 does not cross or touch the curve with equation y=2px^2-6px+4p, where p is a constant.(a) Show that 4p^2-20p+9<0 (b) Hence find the set of possible values for p.


Solve dy/dx= (x√(x^2+3))/e^2y given that y=0 when x=1, giving your answer in the form y = f(x)


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