y =f(x) R 1. Let f be the function given by f(x) = -5-+ 3cos(x) Let R be the shaded region in the second 4 quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line tangent to the graph of f at x = 0, as shown above. (a) Find the area of R. (b) Find the volume of the solid generated when R is rotated about the horizontal line y = -2. (c) Write, but do not evaluate, an integral expression that can be used to find the area of S.
y =f(x) R 1. Let f be the function given by f(x) = -5-+ 3cos(x) Let R be the shaded region in the second 4 quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line tangent to the graph of f at x = 0, as shown above. (a) Find the area of R. (b) Find the volume of the solid generated when R is rotated about the horizontal line y = -2. (c) Write, but do not evaluate, an integral expression that can be used to find the area of S.
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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AP Calculus - Surfaces of revolution
Transcribed Image Text:y=f(x)
R
1. Let fbe the function given by f(x) = - - + 3cos(x) Let R be the shaded region in the second
quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the
line tangent to the graph of f at x = 0, as shown above.
(a) Find the area of R.
(b) Find the volume of the solid generated when R is rotated about the horizontal line y = -2.
(c) Write, but do not evaluate, an integral expression that can be used to find the area of S.
Transcribed Image Text:1 (cont.). Let R be the shaded region bounded by the graph of y=Inx and the line y x = - 2, as shown above.
(d) Find the area of R.
(e) Find the volume of the solid generated when R is rotated about the horizontal line y = -3.
(f) Write, but do not evaluate, an integral expression that can be used to find the volume of the solid generated
when R is rotated about the y-axis.
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