Use spherical coordinates to evaluate the triple integral e¯(x²+y²+z²) x² + y² + z² SIS E Answer: = dV, where E is the region bounded by the spheres x² + y² + z² = 4 and x² + y² + z² = 16.

Q: Use spherical coordinates to evaluate /R Vx2 + y² + z² dV , where B is the ball x² + y? + z? < 10 В

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Q: a) Use surface integral to evaluate the surface area of a parabol 2=2-2²-y² that lies above the…

A: To find the surface area of the given paraboloid.

Q: Use spherical coordinates to evaluate x² + y² + z² = 36. I x² + y² dV, where E is the region between…

A: is the region between the spheres and .We have to find .

Q: Use spherical coordinates to evaluate the triple integral e-(z²+y²+z²) I. dV, E Væ2 + y? + 2² where…

A: Evaluation of the triple integral by using spherical coordinates

Q: Use spherical coordinates to evaluate the triple integral /|| 2² + y² + 2² dV, where E is the ball:…

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Q: Find the surface area of that portion of the surface z = V4 -x that lies above the rectangle R in…

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Q: Consider the part of the solid sphere x2 + y2 + z2 ≤ 4 contained in the first octant (the first…

A: I=∫∫E∫  y dvE is bounded by sphere of radius 2 in first octantusing spherical co‐ordinates

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² + y? + z²)dV = B

A: Solve integral by using Cylindrical cordinates

Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² dV, where E is the ball: x² +…

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Q: A solid G is enclosed by the sphere x? + y² + z² = 4, the plane z = 1 and the xy- plane. By using…

A: The region enclosed by the sphere x2+y2+z2=4, whose radius is 2, the plane z=1 and the xy-plane…

Q: Use spherical coordinater to set up the integmal SzdV, the integral SSSz dV, where Q lies between…

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Q: Use spherical coordinates to evaluate the triple integral e-(z²+z²+z²) / x² + y² + z² where E is the…

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Q: Let S be the solid lying inside both the sphere x2+y2+(z-1)2 = 1 and the elliptic cone x2+y2-z2 = 0.…

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Q: Consider a triangle ABC, on each of whose sides equilateral triangles are dra

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Q: 1. Find the area of the portion of the plane Зх — Зу + 2 — 12 that lies inside the cylinder y? + 22…

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Q: 14. (Activity 16.49). Let n Z, and define : Z→ Zn by ó(k)=[k]. (a) Show that Ker(6) = (n). We also…

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Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² ≤ 49. [[[³ E x² + y² + z² dV,…

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Q: Use spherical coordinates to evaluate the triple integral x² + y² + z² ≤ 64. 11. 2² + y² + 2² dV,…

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Q: 2. Let W be the region where x2 + y? + z2 2. Use spherical coordinates to find I (2? + y? + 2?)-i…

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Q: Converting into cylindrical coordinates the integral r9-(x²+y²) 9-a2 ydzdrde 9-x2

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Q: For the area bounded by curves x = y² - 4y and x = 2y-y², a) determine the area. b) calculate the…

A: Given equation  x=y2-4yx=2y-y2 Now finding the point of intersection…

Q: Use spherical coordinates to evaluate fff (9-x² - y2) dV where E is the solid hemisphere E x² + y2 +…

A: To Evaluate: The integral ∫∫∫E9-x2-y2dV where E: x2+y2+z2≤9 , z≥0 using spherical coordinate system.

Q: Use cylindrical coordinates. Evaluate JIS. √x² + y² dv, where E is the region that lies inside the…

A: Evaluate the integral.

Q: 311. Evaluate surface integral where S is hemisphere x² + y² + z² = x² + y² + z² = a², z ≥ 0.…

A: Parametrize the surface and calculate corresponding ds.

Q: 4. Convert the integral from Cartesian coordinates to both cylindrical and spherical coordi- 1-T²…

A: The given problem is to convert the given triple integral in Cartesian coordinates to triple…

Q: Let D be a region of a solid between the sphere x2+y2+(z-1)2 = 1 and the hemisphere x2+y2+z2 = 4,…

A: We need to use relation between cartesian and spherical co ordinate system to find volume