Area and volume Let R be the region in the first quadrant bounded by the graph of f ( x ) = { 1 if 0 ≤ x ≤ 1 2 − x if 1 < x ≤ 4 . 36. Find the volume of the solid generated when R is revolved about the x -axis.
Area and volume Let R be the region in the first quadrant bounded by the graph of f ( x ) = { 1 if 0 ≤ x ≤ 1 2 − x if 1 < x ≤ 4 . 36. Find the volume of the solid generated when R is revolved about the x -axis.
Solution Summary: The author calculates the volume of the solid generated when R is revolved about the x -axis.
Let f(x) = log(x2 + 1), g(x) = 10 – x2, and R be the region bounded by the graphs of f and g, as shown above.a) Find the volume of the solid generated when R is revolved about the horizontal line y = 10.b) Region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is anisosceles right triangle with a leg in R. Find the volume of the solid.c) The horizontal line y = 1 divides region R into two regions such that the ratio of the area of thelarger region to the area of the smaller region is k:1. Find the value of k.Solve all three
Solids of revolution Let R be the region bounded by y = ln x, the x-axis, and the line x = e as shown. Find the volume of the solid that is generated when the region R is revolved about the x-axis.
5. Let R be the region in the first quadrant enclosed by the graph of f(x)=√cosx, the graph of g(x)= e^x, and the vertical line x=pi/2, as shown in the figure above
(a) Write, but do not evaluate, an integral expression that gives the area of R.
(b) Find the volume of the solid generated when R is revolved about the x-axis.
(c) Region R is the base of a solid whose cross sections perpendicular to the x-axis are semicircles with diameters on the xy-plane. Write, but do not evaluate, an integral expression that gives the volume of this solid.
Chapter 6 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
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