This is a question from my textbook that does't have a solution and quite frankly I have no idea what to do. Any tips would be greatly appreciated.

Question

Given the function f defined by f(x) = 9 - x^2. Find the surface area bounded by the curve y = f(x), the x axis and the lines x = 2 and x = 0.

(a) Find the Riemann Sn sum algebraically, obtained by cutting the surface in n intervals of equal width and considering circumscribed rectangles

(b)Evaluate the surface area by finding lim n->infinite Sn

Thank you

Answer 1

for your first part of the question,
area = ∫(9-x^2) dx from x=0 to x=2
= 9x- (1/3)x^3 | from 0 to 2
= 18 - (1/3)(8) - 0
= 18 - 8/3
= 46/3 units^2

The last time I taught Riemann's sums was about 50 years ago, so I will not attempt that part.

Answer 2

Thanks Reiny :)