1. Let fand g be functions given by f(x)=- enclosed by the graphs off and g. x² +2 and g(x) = -x +2. Let R be the region in the first quadrant 2 f(x) == a. Graph the fand g on the same axes and indicate region R. b. Find the area of R. A = $((-2+²+2)-(-x+2) 3 dx 3 c. Find the value of z so that x = z cuts the solid R into two parts of equal area. d. Find the volume of the solid generated when R is revolved around the x-axis. = 5 e. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from f(x) to g(x). Find the volume of the solid. IT f. Find the volume of the solid generated when R is revolved around the y-axis. 1 30 3 g. Find the volume of the solid generated when R is revolved around the line y = -1. g(x)= 0-2 ²2=-x 2x x ²0 'x (x) x-21₁ =
1. Let fand g be functions given by f(x)=- enclosed by the graphs off and g. x² +2 and g(x) = -x +2. Let R be the region in the first quadrant 2 f(x) == a. Graph the fand g on the same axes and indicate region R. b. Find the area of R. A = $((-2+²+2)-(-x+2) 3 dx 3 c. Find the value of z so that x = z cuts the solid R into two parts of equal area. d. Find the volume of the solid generated when R is revolved around the x-axis. = 5 e. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from f(x) to g(x). Find the volume of the solid. IT f. Find the volume of the solid generated when R is revolved around the y-axis. 1 30 3 g. Find the volume of the solid generated when R is revolved around the line y = -1. g(x)= 0-2 ²2=-x 2x x ²0 'x (x) x-21₁ =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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