Question

The area bounded by the curve xy –3x –2y –10 = 0, x-axis and straight lines x = 3, x = 4 is

• A. 16 log 2 –13
• B. 16 log2 –3
• C. 16 log 2 + 3
• D. None of these

Answer 1

Answer: (C)

16 log 2 + 3

Answer 2

xy –3x –2y –10 = 0 ̃ y = $\frac{3x + 10}{x - 2}$

\ area = $\int_{3}^{4}{ydx}$ \ area = $\int_{3}^{4}{\frac{3x + 10}{x - 2}dx}$

area = $\int _ { 3 } ^ { 4 } \frac { 3 ( x - 2 ) + 16 } { x - 2 } d x$ area = $\int_{3}^{4}{\frac{3(x - 2)}{x - 2}dx}$+ $\int_{3}^{4}{\frac{16}{x - 2}dx}$ area = 3$\int_{3}^{4}{dx}$+ 16 $\int_{3}^{4}{\frac{1}{x - 2}dx}$

area = 3 $= \frac { 1 } { 2 } \left[ 9 + \frac { 5 } { 3 } \right] = \frac { 16 } { 3 }$ x )$_ { 3 } ^ { 4 }$ + 16 $\therefore$log(x –2) }$_ { 3 } ^ { 4 }$

Area = 3 + 16 log 2