EXAMPLE 4 The region R enclosed by the curves y = 3x and y = x2 is rotated about the x-axis. Find the volume of the resulting solid. SOLUTION The curves y = 3x and y = x intersect at the points 0, and The region between them, the solid of 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 y- 3x cross-sectional area by subtracting the area of the inner circle from the area of the outer circle: A(x) = 9Tx? - T(x?)2 = y =x Therefore, we have V = A(x) dx = - -[ A(X)

EXAMPLE 4 The region R enclosed by the curves y = 3x and y = x2 is rotated about the x-axis. Find the volume of the resulting solid. SOLUTION The curves y = 3x and y = x intersect at the points 0, and The region between them, the solid of 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 y- 3x cross-sectional area by subtracting the area of the inner circle from the area of the outer circle: A(x) = 9Tx? - T(x?)2 = y =x Therefore, we have 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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