Calculus AB Integration

User Generated

enkenyrvtu471

Mathematics

AP Calculus AB

none

Description

Just need this completed, no textbooks or anything needed, just knowledge of the subject. Work needs to be shown. Either can print it out and fill it out and send back or can be done on notebook paper or really anything. The assignment is on the photos and shouldn't take very long.

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B(x) (7.5, 6) f(x) 1. Write the appropriate notation for each of the problems described for the graph shown. Do Not Solve. (5 points each) (3.6, 3.8) a) The area of the region between f(x) and g(x). b) The volume formed by semi- circle cross sections perpendicular to the x-axis between f(x) and g(x). c) The volume of a solid formed by revolving the region between f(x) and g(x) about the line y = 6. d) The volume of a solid formed by revolving the region between f(x) and g(x) about the line y = -1. e) The line k divides the area between f(x) and g(x) in half. 4. Use the following functions to answer each question below. (5 points each) fy) = (-1)2 + 2 and g(y) = 6 a) Sketch a graph for the region bounded by the functions fand g and determine the point(s) of intersection. b) Find the area of the region between the functions by integrating over the y-axis. c) Find the volume when the region between the functions is revolved about the line y=-1. d) Set-up an integral to represent the volume for a solid formed whose base is the region bounded by the function fand g, using cross sections of squares perpendicular to the y-axis e) Let the line given by h(x)= x-3 intersect f(y) and g(y). Find the area bounded above by h(x), bounded to the right by g(y), and bounded below by fly). 2. Given the functions, f(x) = (x - 2)² +3 and g(x)= x +3, answer each of the following. (s points each). a) Sketch a graph for both functions and clearly label the points of intersection. This should be a non- calculator generated graph. b) Write and solve an integral expression to represent the area between the functions. c) Write a limit expression of Reimann sums to represent the integral expression from part b. d) Determine the volume for the region bounded by f(x) and g(x) rotated about the line x = 1. e) Write an expression to represent the volume for the region bounded by f(x) and g(x) rotated around the line x=-1. 3. Calculator allowed: Use the functions fx) and g(x) shown below to answer each of the following questions. Show all set-ups and work. (5 points each) f(x) = sin(nx) and g(x) = 2x - 8x a) Sketch functions f and g on the same set of axes and label the points of intersection. Write and evaluate an integral expression in terms of x to represent the area of region R which is the region bounded between the functions. b) Find the volume for the region R when rotated about the line y=-4. Round to the nearest thousandth. c) Given that the horizontal line y=-3 intersects the region R, what is the area below this line? d) What is the volume for a solid whose base is R formed by rectangular cross-sections with a height of - e) The vertical line x = intersects the 2 region R. What is the area of the region on the interval [0, 72]?
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