Question

( left(int_{0}^{1} frac{d x}{f(x)} ight)^{-1} leq e^{int_{0}^{1} log f(x) d x} leq int_{0}^{1} f(x) d x ).

          ( left(int_{0}^{1} frac{d x}{f(x)}
ight)^{-1} leq e^{int_{0}^{1} log f(x) d x} leq int_{0}^{1} f(x) d x ).

$( left(int0^1 fracd xf(x) ight)^-1 leq e^int0^1 log f(x) d x leq int0^1 f(x) d x ).$

Added by Wentao C.

Calculus: Early Transcendental Functions

Robert T. Smith, Roland B. Minton 3rd Edition

Chapter 6

Instant Answer

Solved by Expert Shu-Ting Huang

03/18/2024

Step 1

The left inequality can be proven using the Cauchy-Schwarz inequality. The Cauchy-Schwarz inequality states that for any real numbers $a_i$ and $b_i$, we have $(\sum a_i b_i)^2 \leq (\sum a_i^2)(\sum b_i^2)$. We can apply this inequality to the functions Show more…

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