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Evaluate the iterated triple integral ∫ 1 0 ∫ 1+x √ x √ ∫ xy 0 y −1 zdzdy, dx =

User Frosty
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Answer: We can evaluate the iterated integral in the following order:

First, we integrate with respect to z from 0 to xy:

∫ xy 0 y^(-1)z dz = 1/2y^(-1)z^2 |_0^xy = 1/2x^2

Next, we integrate the result with respect to y from 1 to x:

∫ 1+x 1 1/2x^2 dy = 1/2x^2[y]_1^(1+x) = 1/2x^2(1+x-1) = x^3/4

Finally, we integrate the previous result with respect to x from 0 to 1:

∫ 1 0 x^3/4 dx = 1/4 * x^4/4 |_0^1 = 1/16

Therefore, the value of the iterated triple integral is 1/16.

User Screndib
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