Calculate the following triple-integral in three steps: 12xyxdxdydz Be careful a

Question

Calculate the following triple-integral in three steps: 12xyxdxdydz Be careful about the order of the integration. The first step gives the double-integral f(y, z)dydz, where f(y, z) = Answer is an Expression in y and z The second step gives the integral g(z)dz, Where g(z) = Answer is a Expression in z The last step gives you the final answer which is: Answer is a Number

Explanation / Answer

1.) 12/2 (x^2)yz and limits x=0 to x=2y+z => f(y,z) = 24z*y^3 + 6y*z^3 + 24y^2*z^2 2.) similarly integrating this with respect to y and putting the limits y=0 to y=3z we get, g(z) = 729z^5 3.) integrating this we get the above triple integral = 729/6 = 121.5

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