(d) If R is the region bounded by y = x² and y = 2x² – 4, then / f(x,y) dA as-Ran iterated integral is (just set up, do not evaluate)

Answered: (d) If R is the region bounded by y =…

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

Section10.6: The Three-dimensional Coordinate System

Problem 40E: For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b...

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(d) If R is the region bounded by y = x² and y = 2x² – 4, then / f(x,y) dA as
-
R
an iterated integral is (just set up, do not evaluate)

Expert Solution

Step 1

Given,

$y = x^{2} y = 2 x^{2} - 4$

Step 2

Find limits of x and y we get,

Equate both the equation's we get,

$x^{2} = 2 x^{2} - 4$

Add both sides of the equation by 4 we get,

$x^{2} + 4 = 2 x^{2} - 4 + 4 x^{2} + 4 = 2 x^{2}$

Subtract both sides of the equation by x² we get,

$- x^{2} + x^{2} + 4 = 2 x^{2} - x^{2} 4 = x^{2} x = \pm \sqrt{4} x = \pm 2$

Therefore limit of x is $- 2 \leq x \leq 2$

Now limits of y are,

$2 x^{2} - 4 \leq y \leq x^{2}$

Step by step

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A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64, find the ratio of their a surface areas. b volumes.

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(d) If R is the region bounded by y = x² and y = 2x² – 4, then | S(x, y) dA as R an iterated integral is (just set up, do not evaluate)