JEE Mains · Maths · STD 12 - 8. Application and integration
Let \(A\) be the area of the region \(\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}\) Then \(540\,A\) is equal to
- A \(24\)
- B \(25\)
- C \(23\)
- D \(22\)
Answer & Solution
Correct Answer
(B) \(25\)
Step-by-step Solution
Detailed explanation
\(A=2 \int \limits_{\frac{1}{3}}^{\frac{1}{2}}\left(2 x-2 x^2-(1-x)^2\right) d x\) \(=2\left[2 x^2-x^3-x\right]_{1 / 3}^{1 / 2}\) \(\therefore A=\frac{5}{108} \Rightarrow 540\,A=\frac{5}{108} \times 540=25\)
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