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

3282 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve is defined by the parametric equations x = 3 - 4t, and y = 1 + 2/t. Find dy/dx in terms of t.


The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.


The Curve, C, has equation: x^2 - 3xy - 4y^2 +64 =0 Find dy/dx in terms of x and y. [Taken from Edexcel C4 2015 Q6a]


How do I find a stationary point on the curve?


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