यदि fleft(frac{x-4}{x-2}right)=2x+1,x in R-{1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) दिया गया है $f\left(\frac{x-4}{x-2}\right)=2x+1$. माना $y = \frac{x-4}{x-2}$. तब $y = \frac{x-2-2}{x-2} = 1 - \frac{2}{x-2}$. अतः,$\frac{2}{x-2} =

Vedclass · Accepted Answer

$5x-4 \log |x-1|+c$,जहाँ $c$ समाकलन स्थिरांक है।

Vedclass · Answer

(A) दिया गया है $f\left(\frac{x-4}{x-2}\right)=2x+1$. माना $y = \frac{x-4}{x-2}$. तब $y = \frac{x-2-2}{x-2} = 1 - \frac{2}{x-2}$. अतः,$\frac{2}{x-2} = 1-y$,जिसका अर्थ है $x-2 = \frac{2}{1-y} = \frac{-2}{y-1}$. इस प्रकार,$x = 2 - \frac{2}{y-1} = \frac{2y-2-2}{y-1} = \frac{2y-4}{y-1}$. अब,$f(y) = 2x+1 = 2\left(\frac{2y-4}{y-1}\right) + 1 = \frac{4y-8+y-1}{y-1} = \frac{5y-9}{y-1} = \frac{5(y-1)-4}{y-1} = 5 - \frac{4}{y-1}$. इसलिए,$f(x) = 5 - \frac{4}{x-1}$. अब,$\int f(x) dx = \int \left(5 - \frac{4}{x-1}\right) dx = 5x - 4 \log |x-1| + c$.

यदि $f\left(\frac{x-4}{x-2}\right)=2x+1$,$x \in R-\{1, 2\}$ है,तो $\int f(x) dx$ का मान ज्ञात कीजिए।

Similar Questions

$\int \frac{dx}{\sqrt{7-6x-x^2}}$ का मान ज्ञात कीजिए।

$\int \frac{1 + \tan x \tan(x + a)}{\tan x \tan(x + a)} dx =$

यदि $\int {\frac{{{a^x}{e^{3x}}}}{{{b^x}{c^x}}}} dx = \frac{1}{P}\left( {\frac{{{a^x}{e^{3x}}}}{{{b^x}{c^x}}}} \right) + K$; तो $P =$ ?

$\int \frac{\sin 7x}{\sin 2x \sin 5x} dx =$

निम्नलिखित समाकलन ज्ञात कीजिए: $\int \sec x(\sec x+\tan x) \, dx$

Vedclass Test Series

Exam Paper Generator

Online Exam Module