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Multivariable Calculus

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MVCALC-2XOIGJ

For continuous function $f$ on interval $[a,b]$ with $f(x)>0$, which of the following statements are TRUE?

$$I: \Big(\int_a^b f(x)dx\Big)^2 \leq (b-a)\int_a^b f^2(x) dx$$

$$II: \int_a^b f(x)dx \int_a^b\frac{1}{f(x)}dx \geq (b-a)^2$$

A

Only $I$

B

Only $II$

C

Both $I$ and $II$

D

Neither $I$ nor $II$

E

Not enough information to determine