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The function 3*x^(2/3)-2*x graphs fine, d/dx set to zero in solve app finds extremum at (1,1).

When integrating, regardless if I use x^(2/3) or 3 root x fails.

In the plot, area under curve from 0 to 3.375 yield an answer ~.08+ vs? real answer of ~2.28.

Is this a bug?

Side note...same function integrates fine away from 0.

Integrating 3*x^(2/3)-2*x from 1 to 2 gives correct .91464378706 11 digit answer in ~5 seconds.

Integrating same function written as 3*(3 root x)^2-2*x gives same answer in ~21 seconds.

Taking area under curve in plot app from 1 to 2 gives same correct 11 digit answer almost instantaneously!

I'm not quite duplicating your results.

On the home screen, integrating from 0 to 3.375 my 39gII gives me the ~2.28. In the function app, the signed area from 0 to 3.375 gives me "Undefined." Going from 0.001 to 3.375 gives me ~2.28.

Edit: I do get your results integrating from 1 to 2.