Question

Area bounded by y = g(x), x-axis and the lines x = -2, x = 3, where $g ( x ) = \left\{ \begin{array} { c c } \operatorname { maxi } : \{ f ( t ) ; - 2 \leq t \leq x \} , & - 2 \leq x < 0 \\ \operatorname { mini } : \{ f ( t ) ; 0 \leq t \leq x \} , & 0 \leq x \leq 3 \end{array} \right.$ and f(x)

= x²− |x|, is equal to

• A. $\frac { 113 } { 24 }$sq. units
• B. $\frac { 111 } { 24 }$ sq. units
• C. $\frac { 117 } { 24 }$ sq. units
• D. $\frac { 121 } { 24 }$sq. union

Answer 1

Answer: (A)

$\frac { 113 } { 24 }$sq. units

Answer 2

Clearly g(x) =

s

$\Delta = \int _ { - 2 } ^ { 0 } 2 d x + \int _ { 0 } ^ { 1 / 2 } \left( x - x ^ { 2 } \right) d x + \int _ { 1 / 2 } ^ { 3 } \frac { 1 } { 4 } d x$