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^ direct link above
I showed the right hand side, but I don't know how I would show left. The minimum value that sin^2(x) can be is 0, but that just messes things up.
The only problem here is that you plugged in a value for x in the integral before you evaluated it leave x in the integral and you can show that\[\int xdx\]is in the range you are looking for. Since sin^2 can only make the value smaller, the integral will always be in that range
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also sin^2 cannot be zero because the interval is from pi/4 to pi/2, and sin>0 in that range
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