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Find the volume V inside both the sphere x² + y² +z² = 1 and the cone z = V/x² + y².

Find the volume V inside both the sphere x² + y² +z² = 1 and the cone z = V/x² + y².

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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Please answer question 4. Please give full explanation to the answer. 

4. Find the volume V inside both the sphere x² + y² + z² = 1 and the cone z = Vx² + y². 5. Prove formula (3.25). 6. Prove formula (3.26). 7. Evaluate f sin (*) cos (*,") dA, where R is the triangle with vertices (0,0), (2,0) and R (1,1). (Hint: Use the change of variables u = (x+ y)/2, v = (x – y)/2.) 8. Find the volume of the solid bounded by z = x² + y² and z² = 4(x² + y²). 9. Find the volume inside the elliptic cylinder +=1 for 0<z<2.
Transcribed Image Text:4. Find the volume V inside both the sphere x² + y² + z² = 1 and the cone z = Vx² + y². 5. Prove formula (3.25). 6. Prove formula (3.26). 7. Evaluate f sin (*) cos (*,") dA, where R is the triangle with vertices (0,0), (2,0) and R (1,1). (Hint: Use the change of variables u = (x+ y)/2, v = (x – y)/2.) 8. Find the volume of the solid bounded by z = x² + y² and z² = 4(x² + y²). 9. Find the volume inside the elliptic cylinder +=1 for 0<z<2.
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