I'm practicing for the GRE subject test and this was one of the questions I missed. I know that the answer is $^{3}/_{4}$, but I'm not quite sure why. One thing I thought of is that the average values for each y and z are $^{1}/_{2}$ so that their product is $^{1}/_{4}$, and of course $^{3}/_{4}$ of the interval consists of numbers greater than $^{1}/_{4}$. However, I have absolutely no rigorous justification. What would the rigorous argument be?
On a side note, I have solutions for the two most recent subject tests, but not the test administered in 1993. Can anyone point me toward one? Thanks!
Hint: compute $$ \int_0^1\int_0^1\int_{yz}^11dxdydz. $$