n 9. Consider the following triple integral I = fff zdxdydz, S where the domain S lies

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9. Consider the following triple integral I = fff zdxdydz, S where the domain S lies in the first octant (i.e., x, y, z 20) between the two surfaces z = x²+y² and x²+y²+z² = 2. (a) Express the integral as repeated integrals using Cartesian coordinates. (b) Express the integral as repeated integrals using cylindrical coordinates. (c) Express the integral as repeated integrals using spherical coordinates. (d) Calculate the triple integral using one of the three coordinate systems. (f) Using the result of (d), or otherwise, calculate the following integral J = fff (z+xsin (y²)) dxdydz, SSS where the domain T' lies between the two surfaces z = x²+y² and x²+y²+z² = 2. 9. Consider the following triple integral I = fff zdxdydz, S where the domain S lies in the first octant (i.e., x, y, z 20) between the two surfaces z = x²+y² and x²+y²+z² = 2. (a) Express the integral as repeated integrals using Cartesian coordinates. (b) Express the integral as repeated integrals using cylindrical coordinates. (c) Express the integral as repeated integrals using spherical coordinates. (d) Calculate the triple integral using one of the three coordinate systems. (f) Using the result of (d), or otherwise, calculate the following integral J = fff (z+xsin (y²)) dxdydz, SSS where the domain T' lies between the two surfaces z = x²+y² and x²+y²+z² = 2.

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