Question

integration with limit 2 to 3 (1/x) DX answer is log 3/2​

Answer 1

Explanation:

int 2 to 3 (1/x) dx

= (log x) 2 to 3

log 3 - log 2

(log a - log b= log a/b)

log3/2

Answer 2

$\displaystyle \sf\int\limits_{2}^{3} \frac{1}{x} \, dx = log \frac{3}{2} \: \: \: \: is \: \: proved$

Given :

$\displaystyle \sf\int\limits_{2}^{3} \frac{1}{x} \, dx$

To find :

The limit

Solution :

Step 1 of 2 :

Write down the given Integral

The given Integral is

$\displaystyle \sf\int\limits_{2}^{3} \frac{1}{x} \, dx$

Step 2 of 2 :

Integrate the integral

$\displaystyle \sf\int\limits_{2}^{3} \frac{1}{x} \, dx$

$\displaystyle \sf =log \: x \bigg|_2^3$

$\displaystyle \sf =log \: 3 - log \: 2$

$\displaystyle \sf =log \: \frac{3}{2}$

Hence proved

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