??

2 (10 points) In this problem you will calculate / x2 + 2 dx by using the formal definition of the definite integral: 0 VOO b :1 f(x) dx = lim 2 f(x;)Ax a k:1 (a) The interval [0, 2] is divided into :1 equal subintervals of length Ax. What is Ax (in terms of n)? Ax = 0.5 (b) The righthand endpoint of the kth subinterval is denoted x: . What is x}: (in terms of k and n)? x}; = (c) Using these choices for x: and Ax, the definition tells us that \"AUG 2 n / x2 + 2 dx = lim 21%;:pr 0 k=1 What is f(x;)Ax (in terms of k and rt)? f(x:)Ax = I? (d) Express 2 f(x;;)Ax in closed form. (Your answer will be in terms of n.) k:1 z f(x:)Ax = k=1 (e) Finally, complete the problem by taking the limit as n > 00 of the expression that you found in the previous part. I'l'OO 2 n f x2 + 2 dx = lim 2 f(x;;)Ax = 0 k:1