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b. The equation of a circle of radius r, centered at the origin (0,0), is given by r² = x² + y² • Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y = sqrt(r^(2)-x^(2)) o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r (You do not need to enter this answer into WebAssign.) o Suppose we wanted to set up the following integral so that V gives the volume of a sphere of radius r V = f (x) dx What would a, b and f(x) be? a = -r b = r f(x) = sqrtr^(2)-x^(2) (WebAssign note: remember that you enter π as pi) o Carry out the integration, and calculate the value of V in terms of r. V = (4pir^(3))/3

b. The equation of a circle of radius r, centered at the origin (0,0), is given by r² = x² + y² • Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y = sqrt(r^(2)-x^(2)) o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r (You do not need to enter this answer into WebAssign.) o Suppose we wanted to set up the following integral so that V gives the volume of a sphere of radius r V = f (x) dx What would a, b and f(x) be? a = -r b = r f(x) = sqrtr^(2)-x^(2) (WebAssign note: remember that you enter π as pi) o Carry out the integration, and calculate the value of V in terms of r. V = (4pir^(3))/3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I am not quite sure how to find f(x) at the bottom. Help would be much appreciated! thank you

a. Calculate the volume of the solid of revolution created by rotating the curve y = 4+4 exp(-2 x) about the x-axis, for x between 3 and 6. Volume: 150.93 b. The equation of a circle of radius r, centered at the origin (0,0), is given by r² = x² + y² O Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y = sqrt(r^(2)-x^(2)) o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r? (You do not need to enter this answer into WebAssign.) • Suppose we wanted to set up the following integral so that V gives the volume of a sphere of radius r rb V = S What would a, b and f(x) be? a = -r b = r f(x) f (x) dx = sqrtr^(2)-x^(2) X (WebAssign note: remember that you enter π as pi) o Carry out the integration, and calculate the value of V in terms of r. V = (4pir^(3))/3
Transcribed Image Text:a. Calculate the volume of the solid of revolution created by rotating the curve y = 4+4 exp(-2 x) about the x-axis, for x between 3 and 6. Volume: 150.93 b. The equation of a circle of radius r, centered at the origin (0,0), is given by r² = x² + y² O Rearrange this equation to find a formula for y in terms of x and r. (Take the positive root.) Equation: y = sqrt(r^(2)-x^(2)) o What solid of revolution is swept out if this curve is rotated around the x axis, and x is allowed to vary between -r and r? (You do not need to enter this answer into WebAssign.) • Suppose we wanted to set up the following integral so that V gives the volume of a sphere of radius r rb V = S What would a, b and f(x) be? a = -r b = r f(x) f (x) dx = sqrtr^(2)-x^(2) X (WebAssign note: remember that you enter π as pi) o Carry out the integration, and calculate the value of V in terms of r. V = (4pir^(3))/3
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