Question

2. (-/5 Points) DETAILS 0/2 Submissions Used ASK YOUR Use the upper and lower sums to approximate the area of the region using the given number of subintervals (of equal width). (Round your answers to three decimal places.) y-ſix upper sum lower sum

Answer 1

Consider the following function: y=Vi-x? From the graph given to use we could observe that the total number of subintervals are n= 5 First we need to find the width for each of the sub intervals: The given interval is a =0,b=1 and n=5 Therefore; b-a 1-0 Ar = = 0.2 5 Divide the interval [0,1] in n=5 equal subintervals oflength Ar=0.2 So, we have: a=[0,0.2],[0.2,0.4],[0.4,0.6), (0.6,0.8), (0.8, 1] = b = n

Now, find the upper and the lower sum. For the upper sum we need to use the left endpoints of each of the sub-intervals that we found above. Uppersum = Ar[ y(0) + y(0.2)+ y(0.4) + y(0.6)+ y(0.8)] = 0.21 v1–02 + v1 – (0.2)* + +1-(0.4)* + v1-(0.6)* + v1-(0.8) | = 0.2[1+V0.96 + V0.84 + +0.64 +0.36 + 0.8592 For the lower sum we need to use the right end points of the sub-intervals that we found above. Lower sum = Ax[ y(0.2) + y(0.4)+ y(0.6) + y(0.8) + y(1)] 2.2[v1-(0.2)* + p1-(0.49 + v1-(0.6)* + v1-(0.8)+ v1–1] = 0.2[V0.96 + v0.84 + v0.64 + +0.36 +0] 20.6592