The area enclosed by the curves y=8 x-x^2 and 8 x-4 y+11=0 is

Step-by-step solution

Given equation of curves are aligned & y=8 x-x^2 & 8 x-4 y+11=0 aligned Eq. (i) can be rewritten as aligned & y=- (x^2-2 4 x+4^2-4^2 ) & y=- [(x-4)^2-16 ] & y-16=-(x-4)^2 & aligned (x-4)^2=-(y-16) , which represent a parabola open downward and having vertex at (4,16) . Clearly, Eq. (ii) represent a straight line passing through (0, 11 4 ) and (- 11 8 , 0 ) Let us find the point of intersection of given curves, for this substitute the value of y from Eq. (i) in Eq. (ii). array rlrl & 8 x-4 (8 x-x^2 )+11 =0 & 8 x-32