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6. HOMEWORK (1) Approximate f01$2dzc using (a) left endpoints, (b) right endpoints, (c) midpoints and n = 1000 partitioning intervals. Explain what technology you used in the estimate. Fill out this table. type approximation error left right midpoint (2) Let F(5E) = fom sin t2dt. Sketch an approximate graph of F on the interval [OH/ by lling out this table and then plotting the cOrreSponding points. To ll out each eld in this table using the midpoint approximation with n = 100 intervals. Explain what technology you used. (3) Use the error estimate formula to determine how many partitioning intervals is needed to ensure that the Midpoint Rule approximations for L3 ixdm are accurate to within 0.01. (4) (a) Graph 3; = V1 :32. l (b) Partitioning into how many intervals does insure that f 2 V 1 $2da: can be approx NIH imated using Midpoint rule to within 0.01? l (G) Then use technology to compute an approximation of A = If; v1 3:2d9: accurate 2 to within 0.01. ((1) Finally calculate the number p = (A g) . What number does 6p approximate