MAT 126 Midterm: MAT 126 SBU Exam 126 1 S06 Solution
31 Jan 2019
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Answer each question in the space provided and on the reverse side of the sheets. Unless otherwise indi- cated, answers without justi cation will get little or no partial credit! Cross out anything that grader should ignore and circle or box the nal answer: (a) (10 points) estimate the area under the graph of f (x) = 16 x2 from x = 0 to x = 4 using four rectangles and right endpoints. R4 = f (1) + f (2) + f (3) + f (4) = 15 + 12 + 7 = 34. The function f (x) is concave downward, so that r4 < a, i. e. , it is an underestimate (sketch the graph!) (b) (10 points) repeat part (a) using left endpoints. It is an overestimate, l4 > a (sketch the graph!: (a) (10 points) evaluate integral by interpreting it as area. It is the upper half of the circle of radius 5 cen- tered at the origin, so.
