JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(\left\{(x, y): y^2 \leq 4 x, x<4, \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0, x \neq 3\right\}\) is
- A \(\frac{16}{3}\)
- B \(\frac{64}{3}\)
- C \(\frac{8}{3}\)
- D \(\frac{32}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{32}{3}\)
Step-by-step Solution
Detailed explanation
\( y^2 \leq 4 x, x<4 \) \( \frac{x y(x-1)(x-2)}{(x-3)(x-4)}>0\) \(\text { Case-I : y>0 }\) \(\frac{x(x-1)(x-2)}{(x-3)(x-4)}>0\) \(x \in(0,1) \cup(2,3)\) \(\text { Case - II : y<0 }\) \(\frac{x(x-1)(x-2)}{(x-3)(x-4)}<0, x \in(1,2) \cup(3,4)\)…
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