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Throughout this problem, consider R to be the region between the curves f(x) g(x)=√x in the first quadrant, sliced horizontally (see graph below). x and

Throughout this problem, consider R to be the region between the curves f(x) g(x)=√x in the first quadrant, sliced horizontally (see graph below). x and

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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Question 4 Throughout this problem, consider R to be the region between the curves f(x) = x² and g(x)=√x in the first quadrant, sliced horizontally (see graph below). Y y = √√√x J Δy y = x² X a. Find the exact area between the two curves in R. Show your steps and explain your reasoning. You do not need to simplify your answer. b. Set up an integral for the volume of the solid obtained by rotating R around the x-axis. You do not need to evaluate the integral. c. Set up an integral for the volume of the solid obtained by rotating R around the line x = -1. You do not need to evaluate the integral. Notes: In parts b, and c your explanation should include: i. a rough sketch of the solid of revolution, ii. Label your solid and show the radius(es), iii. Clearly state the method you are using and why, and iv. Clearly show and justify your steps for setting up your integral. Your final integral should be clearly shown.
Transcribed Image Text:Question 4 Throughout this problem, consider R to be the region between the curves f(x) = x² and g(x)=√x in the first quadrant, sliced horizontally (see graph below). Y y = √√√x J Δy y = x² X a. Find the exact area between the two curves in R. Show your steps and explain your reasoning. You do not need to simplify your answer. b. Set up an integral for the volume of the solid obtained by rotating R around the x-axis. You do not need to evaluate the integral. c. Set up an integral for the volume of the solid obtained by rotating R around the line x = -1. You do not need to evaluate the integral. Notes: In parts b, and c your explanation should include: i. a rough sketch of the solid of revolution, ii. Label your solid and show the radius(es), iii. Clearly state the method you are using and why, and iv. Clearly show and justify your steps for setting up your integral. Your final integral should be clearly shown.
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