Barrons AP Calculus

(A) We  see from    the figure  that    ΔA  =   (y 2    −   y 1 )Δx;

(A) Let u   =   x^2     +   2.  Then

and

(A)  From    the     integral    we  get    a    =   −1,    b    =   3,  so  and    

. Replace x with xk and replace dx with Δx
in the integrand to get the general term in the summation.