Question

The area of the closed figure bounded by

x = – 1, x = 2 and y = and the x-axis is -

• A. $\frac { 16 } { 3 }$sq unit
• B. $\frac { 10 } { 3 }$sq unit
• C. $\frac { 13 } { 3 }$sq unit
• D. $\frac { 7 } { 3 }$sq unit

Answer 1

Answer: (A)

$\frac { 16 } { 3 }$sq unit

Answer 2

Required area

A = $\int _ { - 1 } ^ { 1 } \left( - x ^ { 2 } + 2 \right) d x$ +

= $\left[ - \frac { x ^ { 3 } } { 3 } + 2 x \right] _ { - 1 } ^ { 1 }$ + $\left[ x ^ { 2 } - x \right] _ { 1 } ^ { 2 }$

= $\frac { 10 } { 3 }$ + 2 = $\frac { 16 } { 3 }$ sq. units