2 f(x) 2 (6,2) R 20 6 g(x) 8 X 2 and y The functions f and g are given by y = √x = 8 - x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure above. The region R is the base of a solid. For each y, where 0 ≤ y ≤ 2, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Write and evaluate an integral expression that gives the volume of the solid.

2 f(x) 2 (6,2) R 20 6 g(x) 8 X 2 and y The functions f and g are given by y = √x = 8 - x. Let R be the region bounded by the x-axis and the graphs of f and g, as shown in the figure above. The region R is the base of a solid. For each y, where 0 ≤ y ≤ 2, the cross section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Write and evaluate an integral expression that gives the volume of the solid.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.5: Equations Of Lines

Problem 50E: The y-axis along with the graphs of y=-2x+7 and y=x+2 encloses a triangular region. Find the area of...

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