First slide

Evaluation of definite integrals

Question

The least value of the function $F (x) =$
$\int_{x}^{2} \log_{1 / 3} t d t, x \in [1 / 10, 4]$ is at $x =$

Moderate

A

$1 / 10$
B

4
C

1
D

none of these

Solution

$F^{'} (x) = - \log_{1 / 3} x = \frac{\log x}{\log 3} .$ So $F^{'} (x) < 0$ for $\frac{1}{10}$
$< x < 1$ and $F^{'} (x) > 0$ for $x > 1 .$ Hence $f$ has least value at $x = 1 .$

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