EXAMPLE 4 The region R enclosed by the curves y = 2x and y = x is rotated about the x-axis. Find the volume of the resulting solid. SOLUTION The curves y = 2x and y = x intersect at the points (0, and (2. The region between them, the solid of y-2x rotation, and a cross section perpendicular to the x-axis are shown in the figures. A cross-section in the plane P, has the shape of a washer (an annular ring) with inner radius and an outer radius ,so we find the cross-sectional area by subtracting the area of the inner circle from the area of the outer circle: y-? A(x) = 4nx - m(x2)2 = Therefore, we have (4x - x) dx V = A(x) dx = A(X)

EXAMPLE 4 The region R enclosed by the curves y = 2x and y = x is rotated about the x-axis. Find the volume of the resulting solid. SOLUTION The curves y = 2x and y = x intersect at the points (0, and (2. The region between them, the solid of y-2x rotation, and a cross section perpendicular to the x-axis are shown in the figures. A cross-section in the plane P, has the shape of a washer (an annular ring) with inner radius and an outer radius ,so we find the cross-sectional area by subtracting the area of the inner circle from the area of the outer circle: y-? A(x) = 4nx - m(x2)2 = Therefore, we have (4x - x) dx V = A(x) dx = A(X)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 53E

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