Originally Posted by

**BobP** Hi Drexel28

Could you expand on your objection to the statement I made in my earlier post ?

The example you give, $\displaystyle \int^{1}_{-1}x^{3}dx=0,$ doesn't contradict my statement.

My statement would say that the integral is equal to zero $\displaystyle \bold{either}$ because the integrand is identically zero, (which clearly it isn't),$\displaystyle \bold{or}$ because the part of the area lying above the x-axis is equal to the part of the area lying below the x-axis, (which is the case here).

The implication of that is that $\displaystyle f(x)=x^{3}$ is zero at at least one point in the interval, (in order that the curve crosses the x-axis).