int_5^{10} frac{d x}{(x-1)(x-2)} = | vedclass

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(D) ધારો કે $I = \int_5^{10} \frac{d x}{(x-1)(x-2)}$.આંશિક અપૂર્ણાંકનો ઉપયોગ કરતા,$\frac{1}{(x-1)(x-2)} = \frac{1}{x-2} - \frac{1}{x-1}$.$I = \int_5^{

Vedclass · Accepted Answer

$\log \left|\frac{32}{27}\right|$

Vedclass · Answer

(D) ધારો કે $I = \int_5^{10} \frac{d x}{(x-1)(x-2)}$.આંશિક અપૂર્ણાંકનો ઉપયોગ કરતા,$\frac{1}{(x-1)(x-2)} = \frac{1}{x-2} - \frac{1}{x-1}$.$I = \int_5^{10} \left( \frac{1}{x-2} - \frac{1}{x-1} ight) d x$.$I = [\log |x-2| - \log |x-1|]_5^{10}$.$I = [\log |\frac{x-2}{x-1}|]_5^{10}$.$I = \log |\frac{10-2}{10-1}| - \log |\frac{5-2}{5-1}|$.$I = \log |\frac{8}{9}| - \log |\frac{3}{4}|$.$I = \log |\frac{8}{9} 	imes \frac{4}{3}| = \log |\frac{32}{27}|$.

$\int_5^{10} \frac{d x}{(x-1)(x-2)} = $

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