A plane region is bounded by the curvesy² - 4x + 12 = 0 and 4y = (x - 3)². a) Draw a sketch of the plane region. Emphasize the boundaries of the region specially the point of intersections of the curves. b) Obtain the area of the plane region by integration. Set up and evaluate the appropriate integral. You may use a calculator to perform basic arithmetic operations. Express your answers in fraction. c) Find the volume of the solid of revolution generated when the plane region is revolved about the x-axis. d) Calculate by integration the volume of the solid generated when the plane region is rotated about the line x = 1.

A plane region is bounded by the curvesy² - 4x + 12 = 0 and 4y = (x - 3)². a) Draw a sketch of the plane region. Emphasize the boundaries of the region specially the point of intersections of the curves. b) Obtain the area of the plane region by integration. Set up and evaluate the appropriate integral. You may use a calculator to perform basic arithmetic operations. Express your answers in fraction. c) Find the volume of the solid of revolution generated when the plane region is revolved about the x-axis. d) Calculate by integration the volume of the solid generated when the plane region is rotated about the line x = 1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.7: Applied Problems

Problem 58E

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