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

NK
Answered by Natassja K. Maths tutor

3368 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How does one find the equation of a line passing through 2 points of a graph?


How to find and classify stationary points (maximum point, minimum point or turning points) of curve.


Find the integral of ln x


Integrate 1/x


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences