Find the area enclosed between C, the curve y=6x-x^2, L, the line y=16-2x and the y axis.
First we need to find the intersection point(s) of L and C so set 6x-x2=16-2x and rearrange to get x2-8x+16=0 so (x-4)2=0.Repeated root so line is tangent to the curve at x=4, y=16-2(4)=8 that is the point (4,8).Area= integral between 0 and 4 (16-2x) dx - integral between 0 and 4 (6x-x2) dx= [16x - x2 - 3x2 + x3/3] evaluated between 0 and 4= 64/3
DM
Related Maths A Level answers
All answers ▸A quantity N is increasing with respect to time, t. It is increasing in such a way that N = ae^(bt) where a and b are constants. Given when t = 0, N = 20, and t = 8, N = 60, find the value: of a and b, and of dN/dt when t = 12
Find the curve whose gradient is given by dy/dx=xy and which passes through the point (0,3)
Integrate sinxcosx dx
Integrate y= x^3+3x^2-4x-7 between x values 1 and 3