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Homework5: Problem 1 Previous Problem Problem List Next Problem (1 point) More on Areas. Fan'ner Jones. and his wife. Dr. .Jones, both mathematicians. decide to build a fence in their field to keep the sheep safe. Being mathematician: they decide that the fences are to be in the shape of the parabolas y = 8x2 and y = 3:2 + 2. What is the area of the enclosed region? Preview My Answers You have attempted this problem 1 time. Your overall recorded score is 0%. You have unlimited attempts remaining. Homework5: Problem 2 Previous Problem Problem List Next Problem (1 point) Sketch the region enclosed by the curves x = 36 y2 and x = y2 36. Decide whether to integrate with respect to x or y. Then find the area of the region. Area: Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Homework5: Problem 3 Previous Problem Problem List Next Problem (1 point) Find the area of the region between the curves y = |x| and y = x2 2. Area between curves = Preview My Answers Submit Answers Homework5: Problem 4 Previous Problem Problem List Next Problem (1 point) Find the area of the shaded region below. Area: Homework5: Problem 5 Previous Problem Problem List Next Problem (1 point) Find the area of the shaded region below. Area: Homework5: Problem 6 Previous Problem Problem List Next Problem (1 point) The boundaries of the shaded region are the yaxis, the line y = 1, and the curve y = {/Tc. Find the area of this region by writing x as a function of y and integrating with respect to y. Area: Homework5: Problem 7 Previous Problem Problem List Next Problem (1 point) Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y = 3x, y = 3x2 Answer:Homework5: Problem 8 Previous Problem Problem List Next Problem (1 point) Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. y = 4x2 , y = x2+7Homework5: Problem 9 Previous Problem Problem List Next Problem (1 point) Consider the area between the graphs )6 + 2y = 19 and x + 5 = y2. This area can be computed in two different ways using integrals b c / f(x) dx + / g(x) dx 2 b wherea: ,b: ,3: and f (x) = 00 = First of all it can be computed as a sum of two integrals Alternatively this area can be computed as a single integral 19 / My) dy where 0' = , ,6 = and My) = Either way we nd that the area is Homework5: Problem 10 Previous Problem Problem List Next Problem (1 point) Find the area of the region enclosed between f(x) = x2 + 6x + 3 and g(x) = 2x2 + 3x 1. Area: ( Note: The graph above represents both functions f and g but is intentionally left unlabeled.) Homework5: Problem 11 Previous Problem Problem List Next Problem (1 point) Find the volume of the solid obtained by rotating the region under the graph of the function f (x) = 4x J:Z about the xaxis over the interval [0,4]. V: Homework5: Problem 12 Previous Problem Problem List Next Problem (1 point) Find the volume of the solid obtained by rotating the region under the graph of the function f (x) = as" about the x-axis over the interval [0, 3]. V: Homework5: Problem 13 Previous Problem Problem List Next Problem (1 point) Find the volume of the solid obtained by rotating the region bounded by x = 2y, y =1, x =0, about the y-axis. Answer:Homework5: Problem 14 Previous Problem Problem List Next Problem (1 point) Find the volume of the solid obtained by rotating the region bounded by y=8x2,x=19y=0, about the x-axis. Answer: Homework5: Problem 15 Previous Problem Problem List Next Problem (1 point) y C(0,1) Flelerring to the figure above, find the volume generated by rotating the region R; about the line 0A. Volume = Homework5: Problem 16 Previous Problem Problem List Next Problem (1 point) Find the volume of the solid formed by rotating the region enclosed by x=o,x=1,y=0,y=8+x3 about the xaxis
