Question

Area bounded by the curves y = , x = 2y + 3 in the first quadrant and x-axis is -

• A. $2 \sqrt { 3 }$
• B. 18
• C. 9
• D. $\frac { 34 } { 3 }$

Answer 1

Answer: (C)

9

Answer 2

The two curves meet where = ... (i)

Ž 4x = x² – 6x + 9 Ž x² – 10 x + 9 = 0 Ž x = 9, 1

But x = 1 does not satisfy (i)

\The two curves meet where x = 9.

\ Required area (shown shaded)

= area OBCO = area OBDCO – area BDC

= dx – $\int _ { 3 } ^ { 9 } \left( \frac { x - 3 } { 2 } \right)$dx

= $\frac { 2 } { 3 }$ [x^3/2 – $\frac { 1 } { 2 }$ $\left[ \frac { x ^ { 2 } } { 2 } - 3 x \right] _ { 3 } ^ { 9 }$= 9.