FInd an interval like [0,a] so that 1/x^1/3 is 1

I have that 1/a time int (0 to a) is 1/x^1/3 so then

1/a * 1.5* a^2/3 =1 and I get a=9/4, but this does not work when I plug it back in....what am I doing wrong here?

Then it tells you to find interval like [0,a] for 1/nth root of x.