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

3170 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the derivative of the following function: f(x) = x(x^3 + 2x)


Find the inverse of the function g(x)=(4+3x)/(5-x)


Solve ∫(x+2)/(2x^2+1)^3 dx


Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.


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