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52. (c) The vertical line x = k divides R into two regions where the area of the region to the left of the line x = k is the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k.

52. (c) The vertical line x = k divides R into two regions where the area of the region to the left of the line x = k is the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The curves f(x) = 3-x² and g(x) = e2 - 1 are shown in the figure. Let R be the shaded region bounded by the graph of f(x), g(x) and the y-axis. 50. (a) Find the area of R using dy as your differential. 51. (b) Find the volume of the solid generated when R is rotated about the x-axis. 52. (c) The vertical line x = k divides R into two regions where the area of the region to the left of the line x = k is the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k.
Transcribed Image Text:The curves f(x) = 3-x² and g(x) = e2 - 1 are shown in the figure. Let R be the shaded region bounded by the graph of f(x), g(x) and the y-axis. 50. (a) Find the area of R using dy as your differential. 51. (b) Find the volume of the solid generated when R is rotated about the x-axis. 52. (c) The vertical line x = k divides R into two regions where the area of the region to the left of the line x = k is the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k.
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