Find the area of the shaded region bounded by y=7x and y=x(sqrt(22^2-x^2))

Answer 1

y=7x and y=x√(484-x^2)
intersect at x=0,±√435
By symmetry, the area is

2∫[0,√435] x√(484-x^2)-7x dx
= 2 (1/6 (x^2-484)(2√(484-x^2) - 21)) [0,√435]
= 3825