Let A be the area of the region (x, y): y ≥ x2, y ≥(1-x)2, y ≤ 2 x(1-x) . Then 540 A is equal to

Question

Let A be the area of the region (x, y): y ≥ x2, y ≥(1-x)2, y ≤ 2 x(1-x) . Then 540 A is equal to  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/745f1b1e805b328234d4b76f5f4509f9-.png" /> A =2 ∫ limits(1/3)(1/2)(2 x-2 x 2-(1- x )2) dx =2[2 x 2- x 3- x ]1 / 31 / 2 ∴ A =(5/108) ⇒ 540 A =(5/108) × 540=25

Q. Let $A$ be the area of the region ${(x, y) : y \geq x^{2}, y \geq (1 - x)^{2}, y \leq 2 x (1 - x)}$ . Then $540 A$ is equal to ______

$A = 2 \frac{1}{3} \int \frac{1}{2} (2 x - 2 x^{2} - (1 - x)^{2}) d x$
$= 2 [2 x^{2} - x^{3} - x]_{1/3}^{1/2}$
$∴ A = \frac{5}{108} \Rightarrow 540 A = \frac{5}{108} \times 540 = 25$

Q. Let A be the area of the region {(x,y):y≥x2,y≥(1−x)2,y≤2x(1−x)}. Then 540A is equal to ______

A=231​∫21​​(2x−2x2−(1−x)2)dx =2[2x2−x3−x]1/31/2​ ∴A=1085​⇒540A=1085​×540=25

Q. Let $A$ be the area of the region ${(x, y) : y \geq x^{2}, y \geq (1 - x)^{2}, y \leq 2 x (1 - x)}$ . Then $540 A$ is equal to ______

$A = 2 \frac{1}{3} \int \frac{1}{2} (2 x - 2 x^{2} - (1 - x)^{2}) d x$
$= 2 [2 x^{2} - x^{3} - x]_{1/3}^{1/2}$
$∴ A = \frac{5}{108} \Rightarrow 540 A = \frac{5}{108} \times 540 = 25$