3. Consider the function f (x) graphed below: yetiA -2 (a) Write a Riemann sum with n = 4 subdivisions approximating ", f (æ) dx using left hand sample points, then evaluate the sum. (b) Write a Riemann sum with n = 4 subdivisions approximating "2 f (x) dæ using right hand sample points, then evaluate the sum. (c) Write a Riemann sum with n = 4 subdivisions approximating ", f (x) dx using midpoint sample points, then evaluate the sum.

(LT2.a) Express the following sum in Sigma notation: 3 4 5 6 + + + +...+ 33 34 36 38 (LT2.b) Consider the following graph of a function g: T -2 2 -2- 4 क 2 17 324 (b) Evaluate the definite integral f g(x) dx. -4 To demonstrate mastery you must show your work. 6 (a) Write out the left Riemann sum L5 for g on the interval [-4, 6] and compute its value.

Graph the function f(x) = x² − 1 over the interval [0, 2]. Partition the interval into four subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum f(CK) Axk, given that c is the (a) left-hand endpoint, (b) right-hand endpoint, (c) midpoint of the kth subinterval. (a) Choose the correct graph below. O A. y (b) Choose the correct graph below. O A. 0 y (c) Choose the correct graph below. 4 B. 0 -2- 4 B. y 3 X X Q ... C. 4 -2- C. 4 0 D. 4 O D. k=1 t

19er q gral (axa +Hy+2)dx a) Find the Riemann sum for this inmtegral