(a) Evaluate the surface integral JL. TU xy ds where D is part of the plane x+y+3z = 3 that lies in the first quadrant. Sketch the region D. I (b) Use triple integral in Cylindrical coordinates to calculate the volume of the solid inside the cylinder x² + y² = 3, bounded above by the sphere x² + y² + z² = 9 and bounded below by the plane z = -1. Sketch the solid. (c) Evaluate the following double integral by switching the order of integration: 3 2 So So In(x)dx dy /y+I Sketch the region of integration.
(a) Evaluate the surface integral JL. TU xy ds where D is part of the plane x+y+3z = 3 that lies in the first quadrant. Sketch the region D. I (b) Use triple integral in Cylindrical coordinates to calculate the volume of the solid inside the cylinder x² + y² = 3, bounded above by the sphere x² + y² + z² = 9 and bounded below by the plane z = -1. Sketch the solid. (c) Evaluate the following double integral by switching the order of integration: 3 2 So So In(x)dx dy /y+I Sketch the region of integration.
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:(a) Evaluate the surface integral
JL. TU
xy ds
where D is part of the plane x+y+3z = 3 that lies in the first quadrant. Sketch
the region D.
I
(b) Use triple integral in Cylindrical coordinates to calculate the volume of the solid
inside the cylinder x² + y² = 3, bounded above by the sphere x² + y² + z² = 9 and
bounded below by the plane z = -1. Sketch the solid.
(c) Evaluate the following double integral by switching the order of integration:
3 2
So So In(x)dx dy
/y+I
Sketch the region of integration.
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