10. Consider the region R in the first quadrant bounded by the parabolas y= 4x and y = 2x.(a) Sketch the region R.(b) Find the area of R.(c) Find the volume of the solid generated when R is revolved around the y-axis.

Answered: 10. Consider the region R in the first…

10. Consider the region R in the first quadrant bounded by the parabolas y = 4x and y 2x. %3D %3D (a) Sketch the region R.

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

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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Question

10. Consider the region R in the first quadrant bounded by the parabolas y= 4x and y = 2x.
(a) Sketch the region R.
(b) Find the area of R.
(c) Find the volume of the solid generated when R is revolved around the y-axis.

Expert Solution

Step 1

10.

Consider the given parabolas $y^{2} = 4 x$ and $y = 2 x^{2}$

Fins the intersection point

$\begin{array}{rcl} {(2 x^{2})}^{2} & = & 4 x \\ 4 x^{4} & = & 4 x \\ x^{4} - x & = & 0 \\ x (x^{3} - 1) & = & 0 \\ x & = & 0, 1 \end{array}$

Now find the value of $y$

$y = 0,$

And

$\begin{array}{rcl} y^{2} & = & 4 (1) \\ y^{2} & = & 4 \\ y & = & 2 \end{array}$

Hence, the intersection point $(0, 0), (1, 2)$

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