Find the area between the two curves y = √ and y= 2r in the half plane z 20

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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10. Geometric applications
(a) Find the area between the two curves y = √ and y = in the half plane x ≥ 0
2x
(b) Let S be the region in the plane between the x axis and the curve y = cos(x²) for 0 ≤ x ≤
√π/2
Use any method to set an integral equal to the volume of the solid obtained by rotating this
region about the y axis.
Then, evaluate this integral.
(c) Let S be the region in the plane below the curve y = 2√/tanz and above the r axis, for
0≤x≤7.
Use any method to set an integral equal to the volume of the solid obtained by rotating this
region about the r axis. Then, evaluate this integral.
Transcribed Image Text:10. Geometric applications (a) Find the area between the two curves y = √ and y = in the half plane x ≥ 0 2x (b) Let S be the region in the plane between the x axis and the curve y = cos(x²) for 0 ≤ x ≤ √π/2 Use any method to set an integral equal to the volume of the solid obtained by rotating this region about the y axis. Then, evaluate this integral. (c) Let S be the region in the plane below the curve y = 2√/tanz and above the r axis, for 0≤x≤7. Use any method to set an integral equal to the volume of the solid obtained by rotating this region about the r axis. Then, evaluate this integral.
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