Question

Area bounded by the curve $xy-3x-2y-10=0,$ x-axis and the lines $x=3,x=4$ is ?

• A. $16\log 2-13$
• B. $16\log 2-3$
• C. $16\log 2+3$
• D. None of these

Answer 1

Answer: (C)

$16\log 2+3$

Given the curve, $xy-3x-2y-10=0\Rightarrow xy-2y=3x+10\Rightarrow y(x-2)=3x+10\Rightarrow y=\frac{3x+10}{x-2}$

$\therefore$ Area bounded by the curve $xy-3x-2y-10=0$, x-axis and the lines $x=3,x=4$,

${\int }_3^4\left|y\right|dx={\int }_3^4\left(\frac{3x+10}{x-2}\right)dx={\int }_3^4\left(\frac{3x-6+16}{x-2}\right)dx={\int }_3^4(3+\frac{16}{x-2})dx={[3x+16\log |x-2|]}_3^4=[12+16\log \left|2\right|-9-16\log \left|1\right|]=16\log 2+3squareunits.$