Area Under Curves Question 9
Question 9 - 30 January - Shift 2
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
Show Answer
Answer: (25)
Solution:
Formula: Area between two curves - Area enclosed between two curves intersecting at two different points
$A=2 \int _{\frac{1}{3}}^{\frac{1}{2}}(2 x-2 x^{2}-(1-x)^{2}) d x$
$A=2[2 x^{2}-x^{3}-x] _{1 / 3}^{1 / 2}$
$\therefore A=\frac{5}{108} \Rightarrow 540 A=\frac{5}{108} \times 540=25$
