Use spherical coordinates to integrate f(x, y, z) = √√x² + y² + z² over the solid E between the spheres x² + y² + z² = 4 and x² + y² + z² = 49. (Give an exact answer. Use symbolic notation and fractions where needed.) √x² + y² + 2² av = E

Q: nter the exact answer. Im z? dz

A: Given, the vertices of the triangle are 0, 2, 2i.

Q: 3. Let OÁ = i +2j+ k, OB = 3i+j+2k and OC = 5i+j+ 3k. (a) i. Find AB × AČ. ii. Find the area of…

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Q: Verify that U(x,y) = x3y - xy3 is harmonic on the complex plane.

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Q: Evaluate ffz + 3y - x^2 ds where S is the portion of z=2-3y+x^2 that lies over the triangle in the…

A: To find the value of given fds over given region.

Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

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Q: Evaluate ([cos (x – y)sin(x+ y)dA, where R is the triangle with vertices (0,0), R (-1,7), and (7,7)…

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.