Question

Area of the region bounded by the curve xy – 3x – 2y – 10 = 0, x – axis, line x = 3 and x = 4

• A. $3+16lo{g}_{e}2$
• B. $16lo{g}_{e}2-3$
• C. $4lo{g}_{e}3-3$
• D. $5lo{g}_{e}2-1$

Answer 1

The correct option is A $3+16lo{g}_{e}2$



$y=\frac{10+3x}{x-2},x\ne 2$
As $x\to 2^{+},y\to \infty x\to 2^{-},y\to -\infty$
Also $\underset{x\to \infty }{lt}y=\underset{x\to \infty }{lt}\frac{\frac{10}{x}+3}{1-\frac{2}{x}}=3$
$\therefore$ Area = ${\int }_3^4\frac{10+3x}{x-2}dx={\int }_3^4\frac{10}{x-2}dx+3{\int }_3^4\frac{x-2+2}{x-2}dx=log{|x-2|}_3^4+3{\{x+2log|x-2|\}}_3^4$
$=10lo{g}_{e}2+3+6lo{g}_{e}2$