Question

The area bounded by $y = - x ^ { 2 } + 2 x + 3$and$y = 0$ is

• A. $32$
• B. $\frac { 32 } { 3 }$
• C. $\frac { 1 } { 32 }$
• D. $\frac { 1 } { 3 }$

Answer 1

Answer: (B)

$\frac { 32 } { 3 }$

Answer 2

Given, $y = - x ^ { 2 } + 2 x + 3$and $y = 0$

Therefore, $x = - 1$ and $x = 3$

∴ Required area $= \int _ { - 1 } ^ { 3 } \left( - x ^ { 2 } + 2 x + 3 \right) d x$

$= \left[ - \frac { x ^ { 3 } } { 3 } + x ^ { 2 } + 3 x \right] _ { - 1 } ^ { 3 } = \frac { 32 } { 3 }$.