The area bounded by y = - x^2 + 2x + 3 and y = 0 is - Vidyadip

MCQ

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

A
$32$
✓
$\frac{{32}}{3}$
C
$\frac{1}{{32}}$
D
$\frac{1}{3}$

✓

Answer

Correct option: B.

$\frac{{32}}{3}$

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

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

Required area $ = \int_{ - 1}^3 {( - {x^2} + 2x + 3)dx} $

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

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