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1. Consider the lune enclosed between x² + y² = 1 and x² + (y+1)² =2. Show the following using calculus. If you wish you may use any computer algebra system you like to do the integrals, just write down each integral and its solution. I 0.5 III II -1 -0.5 a. Use calculus to show that the tangent line to x² + (y+1)² = 2 at the point (-1,0) goes through (0,1). b. Use calculus to show that the area in region I on the graph is equal to half the area of region III. c. Find the area of the lune using calculus. d. Find the area of the lune using Hippocrates' solution. [Naturally, the answers to c and d should be the same.] 0.5

1. Consider the lune enclosed between x² + y² = 1 and x² + (y+1)² =2. Show the following using calculus. If you wish you may use any computer algebra system you like to do the integrals, just write down each integral and its solution. I 0.5 III II -1 -0.5 a. Use calculus to show that the tangent line to x² + (y+1)² = 2 at the point (-1,0) goes through (0,1). b. Use calculus to show that the area in region I on the graph is equal to half the area of region III. c. Find the area of the lune using calculus. d. Find the area of the lune using Hippocrates' solution. [Naturally, the answers to c and d should be the same.] 0.5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider the lune enclosed between x² +y² = 1 and x² + (y+1)² =2. Show the following using calculus. If you wish you may use any computer algebra system you like to do the integrals, just write down each integral and its solution. I 0.5 III II -1 -0.5 a. Use calculus to show that the tangent line to x² + (y+1)² = 2 at the point (-1,0) goes through (0,1). b. Use calculus to show that the area in region I on the graph is equal to half the area of region III. c. Find the area of the lune using calculus. d. Find the area of the lune using Hippocrates' solution. [Naturally, the answers to c and d should be the same.] 0.5
Transcribed Image Text:1. Consider the lune enclosed between x² +y² = 1 and x² + (y+1)² =2. Show the following using calculus. If you wish you may use any computer algebra system you like to do the integrals, just write down each integral and its solution. I 0.5 III II -1 -0.5 a. Use calculus to show that the tangent line to x² + (y+1)² = 2 at the point (-1,0) goes through (0,1). b. Use calculus to show that the area in region I on the graph is equal to half the area of region III. c. Find the area of the lune using calculus. d. Find the area of the lune using Hippocrates' solution. [Naturally, the answers to c and d should be the same.] 0.5
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