3. (25 points) The purpose of this problem is to assess your understanding of the DEFI- NITION OF THE INTEGRAL. In class

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3 25 Points The Purpose Of This Problem Is To Assess Your Understanding Of The Defi Nition Of The Integral In Class 1 (178.94 KiB) Viewed 16 times

3. (25 points) The purpose of this problem is to assess your understanding of the DEFI- NITION OF THE INTEGRAL. In class we defined 5° f(a) de := lim (f(x1) + f(x2)+...+ f(xn)) A.x. N700 where b - a AC and k = a + kAr, N for k = 0,1,2, ... . N. Notice that, for each fixed N, the sum on the right approximates the exact value of the integral. This sum is called a Riemann sum. (a) Use a Riemann sum with N = 6 to approximate ſi vardi. (15+ V +... + (b) The expression 2 50 1 50 + V 50 50 is a Riemann sum. What integral is this sum approximating? (c) Using Riemann sums, explain why V 50 1 3 < 4 s'i dx < 1. 1+x4