sirhc1
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Homework Statement
\int^{1}_{0}\int^{x^2}_{0}\int^{y}_{0} f(x,y,z) dz dy dx
Find 5 equivalent iterated integrals.
Homework Equations
0 ≤ z ≤ y
0 ≤ y ≤ x^2
0 ≤ x ≤ 1
The Attempt at a Solution
1) \int^{1}_{0}\int^{√y}_{0}\int^{x^2}_{0} f(x,y,z) dz dx dy
I will try dz dy dx first.
Because y = x^2, so 0 ≤ z ≤ x^2
Because y = x^2, so 0 ≤ x ≤ √y
And by the same logic, 0 ≤ y ≤ 1
When I integrate for f(x,y,z) = 1, the correct answer is 1/10. I do not get the same answer with my solution. Help! Is it possible to solve this without graphing it? Or is it necessary to get the correct answer?