Discuss the below:
Q1. Let f(x) = x^2-2x+2 on the interval [-1, 2]. Sketch a graph of this function along with the rectangles that would be used to approximate the area under the curve using a right sum with n = 6. Be accurate and make your graph large.
a) Calculate the approximation in stepwise, use appropriate notation.
b) Approximate the area under the graph of f(x) = x^2 - 2x + 2 on the interval [-1, 2]. Using a right sum with n = 24. show all the relevant steps depending upon your approach as above.
c) Do the approximation in (a) and (b) overestimate or underestimate the true area? Explain without finding the actual area.
Q2. Find the exact area under the graph of f(x) = x^2 - 2x + 2 on the interval [-1 , 2] using limits with a right sum. Correct notation is crucial.
Q3. Find the area under the graph of f(x) = x^2 - 2x + 2 on the interval [-1 , 2] using a definite integral.