Set-up the following multiple integrals. Sketch the region/solid of integration c.The triple integral in Cylindrical coordinates that gives the volume of thesolid that lies under the surface z=x+y°+1, above the xy-plane, and insidex²+y? =5. d.The triple integral in Spherical coordinates that gives the volume of thesolid bounded by the plane z=0, the cylinder x +y = 7, and the segment (orportion) of the sphere x+y +z? = 16 above the xy-plane.

Answered: Image /qna-images/answer/1bfd27d4-b889-467e-9e4a-62119a9e66c8.jpg

Answered: c. The triple integral in Cylindrical…

c. The triple integral in Cylindrical coordinates that gives the volume of the solid that lies under the surface z=x+y°+1, above the xy-plane, and inside x+y? =5.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.3: Volume And Average Value

Problem 25E

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Question

Set-up the following multiple integrals. Sketch the region/solid of integration

c.
The triple integral in Cylindrical coordinates that gives the volume of the
solid that lies under the surface z=x+y°+1, above the xy-plane, and inside
x²+y? =5.

d.
The triple integral in Spherical coordinates that gives the volume of the
solid bounded by the plane z=0, the cylinder x +y = 7, and the segment (or
portion) of the sphere x+y +z? = 16 above the xy-plane.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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