The area of the region for which 0

Question

The area of the region for which 0 < y < 3 - 2x - x2 and x > 0 is (A) ∫3-1 (3 - 2x - x2) dx  (B) ∫10 (3 - 2x - x2) dx  (C) ∫31 (3 - 2x - x2) dx  (D) ∫30 (3 - 2x - x2) dx

Tardigrade Admin · Accepted Answer

3 - 2x - x2 > 0 ⇒ x2 + 2x - 3 > 0 ⇒ ( x +3)(x -1) < 0 ⇒ x < 1

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

$\int_{- 1}^{3} (3 - 2 x - x^{2}) d x$

$\int_{0}^{1} (3 - 2 x - x^{2}) d x$

$\int_{1}^{3} (3 - 2 x - x^{2}) d x$

$\int_{0}^{3} (3 - 2 x - x^{2}) d x$

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

Q. The area of the region for which 0<y<3−2x−x2 and x>0 is

∫−13​(3−2x−x2)dx

∫01​(3−2x−x2)dx

∫13​(3−2x−x2)dx

∫03​(3−2x−x2)dx