Question

1(a) . Let A denote the area enclosed by the graph f(x)= 10-x, the x- axis , and the lines x=3 and x =5. Graphing the region and using plane geometry , find A. (b). Let A denote the area enclosed by the graph f(x)= (x-1)^2, the x - axis , and te lines x=2 and x=9. Graphing the region and using plane geometry , we can find that A=. (c). Suppose S4 is the lower sum of the area enclosed by the graph f(x)=2x^2 , the x- axis , and the lines x=0 and x =4 by partitioning [0, 4] into four subintervals [0,1], [1, 2], [2, 3], and [3, 4]. Find S4. (d) , Suppose S4 is the upper sum of the area enclosed the graph f(x) =2x^2 , the x- axis , a d the lines x =0 and x = 4 by partitioning [0,4] into four subintervals [0,1], [1 ,,2], [2, 3], and [3, 4], Find S4

Answer 1

5 CS,S) 2 59 9,64) 2- (2.L 2 t e.

L 2 3 4 28+32 4-60 4-