Verify that sin(x^(1/3)) is an odd function and use that fact to show that...

Question

anonymous · Answer

Verify that $$f(x)=\sin \sqrt[3]{x}$$ is an odd function and use that fact to show that $$0\le \int\limits_{-2}^{3}\sin \sqrt[3]{x}dx \le1$$

I know how to verify of the function is even or odd, but I'm having trouble showing why the inequality is true.

anonymous · Answer

Have you ever tried the mean value theorem??

anonymous · Answer

Hmm. I hadn't thought of that. I can try that and see how it goes.

anonymous · Answer

Actually, I don't know if I can do that. I need to find the antiderivative of the function in order to use the Mean Value Theorem and I'm not even sure how to find the antiderivative of this function.

anonymous · Answer

as far as I know you don't have to find the antiderivative in the mean value theorem! It says that|dw:1389206701737:dw|