Question

The area of the region for which $0 < y < 3 - 2x - x^2$ and $x > 0$ is

• A. $\int^3_{-1} (3 - 2x - x^2) dx $
• B. $\int^1_{0} (3 - 2x - x^2) dx $
• C. $\int^3_{1} (3 - 2x - x^2) dx $
• D. $\int^3_{0} (3 - 2x - x^2) dx $

Answer 1

Answer: (B)

$ 3 - 2x - x^2 > 0 $
$\Rightarrow \, x^2 + 2x - 3 > 0 $
$\Rightarrow ( x +3)(x -1) < 0 \Rightarrow x < 1 $