Find the area under the curve with equation y = 5x - 2x^2 - 2, bounded by the x-axis and the points at which the curve reach the x-axis.

First, we must find the two points at which the curve crosses the boundary. To do this, set y=0 and solve.0 = 5x - 2x2 - 20 = (2x - 1)(-x+2)This gives that x = 0.5 and x = 2Next, we integrate with these boundsI20.5 (5x - 2x2 - 2) dx = [2.5x2 - 2/3 x3 - 2x]20.5 = ( 2.54 - 2/38 - 22 - 2.50.25 + 2/30.125 + 20.5 ) = 1.125

Answered by Natassja K. Maths tutor

3131 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I work out (2+y)^4 using the binomial expansion?


Mechanics 1: How do you calculate the magnitude of impulse exerted on a particle during a collision of two particles, given their masses and velocities.


Integrate y=x^2 between the limits x=3 and x=1


The point A lies on the curve with equation y = x^(1/2). The tangent to this curve at A is parallel to the line 3y-2x=1. Find an equation of this tangent at A. (PP JUNE 2015 AQA)  


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