Question

Area bounded by the curves 4y = |x²− 4| and y + |x| = 7, is equal to

• A. 8 sq. units
• B. 16 sq. units
• C. 4 sq. units
• D. 32 sq. union

Answer 1

Answer: (D)

32 sq. union

Answer 2

Required area,

$= 2 \left( \int _ { 0 } ^ { 2 } \left( 7 - x - \left( \frac { 4 - x ^ { 2 } } { 4 } \right) \right) d x + \int _ { 2 } ^ { 4 } \left( 7 - x - \left( \frac { x ^ { 2 } - 4 } { 4 } \right) \right) d x \right)$

$= 2 \left( \int _ { 0 } ^ { 2 } \left( 6 - x - \frac { x ^ { 2 } } { 4 } \right) d x + \int _ { 2 } ^ { 4 } \left( 8 - x - \frac { x ^ { 2 } } { 4 } \right) d x \right)$

$= 2 \left( 6 x - \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 3 } } { 12 } \right) _ { 0 } ^ { 2 } + 2 \left( 8 x - \frac { x ^ { 2 } } { 2 } - \frac { x ^ { 3 } } { 12 } \right) _ { 2 } ^ { 4 }$

= 32 sq. units.