2. Let R be the region bounded by C1 : y = ar³ + b, C2 : y = cx + b, where a, b, c E R+. (a) Find the area of R. Then find the volume of the solid generated by rotating R around the r-axis. (b) Find two distinct parameterizations of both C1 and C2. (c) Find the area of R again using both parameterizations. All three computations (two from this part and one from part (a)) should match. (d) Find the volume of the same solid from part (a) using both parameterizaitons. All three computations should match.
2. Let R be the region bounded by C1 : y = ar³ + b, C2 : y = cx + b, where a, b, c E R+. (a) Find the area of R. Then find the volume of the solid generated by rotating R around the r-axis. (b) Find two distinct parameterizations of both C1 and C2. (c) Find the area of R again using both parameterizations. All three computations (two from this part and one from part (a)) should match. (d) Find the volume of the same solid from part (a) using both parameterizaitons. All three computations should match.
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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Transcribed Image Text:2. Let R be the region bounded by C1 : y = ax³ + b, C2 : y = cx + b, where a, b, c € R+.
(a) Find the area of R. Then find the volume of the solid generated by rotating R around
the r-axis.
(b) Find two distinct parameterizations of both C1 and C2.
(c) Find the area of R again using both parameterizations. All three computations (two from
this part and one from part (a)) should match.
(d) Find the volume of the same solid from part (a) using both parameterizaitons. All three
computations should match.
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