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No calculators. Using the Disc or Washer method only, find the exact value of the volume of the solid obtained by rotating the region enclosed by y=x² and x = y² about y=1.

No calculators. Using the Disc or Washer method only, find the exact value of the volume of the solid obtained by rotating the region enclosed by y=x² and x = y² about y=1.

Elementary Geometry For College Students, 7e
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 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
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(a) (b) (c) (d) Sketch the two curves on the same graph, and shade in the region between them. Show calculations for intersection points. Sketch the 3D volume that results when you rotate the shaded area from part (a) about y = 1. Draw a typical disc or washer on this 3D sketch. Determine an expression for dV, as shown in lecture. State which variable is your "queen variable", and give a brief explanation. Calculate the exact value of volume V.
Transcribed Image Text:(a) (b) (c) (d) Sketch the two curves on the same graph, and shade in the region between them. Show calculations for intersection points. Sketch the 3D volume that results when you rotate the shaded area from part (a) about y = 1. Draw a typical disc or washer on this 3D sketch. Determine an expression for dV, as shown in lecture. State which variable is your "queen variable", and give a brief explanation. Calculate the exact value of volume V.
No calculators. Using the Disc or Washer method only, find the exact value of the volume of the solid obtained by rotating the region enclosed by y=x² and x=y² about y=1.
Transcribed Image Text:No calculators. Using the Disc or Washer method only, find the exact value of the volume of the solid obtained by rotating the region enclosed by y=x² and x=y² about y=1.
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