JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(f: R \rightarrow R\) be a continuous function. Then \(\lim _{x \rightarrow \frac{\pi}{4}} \frac{\frac{\pi}{4} \int_{2}^{\sec ^{2} x} f(x) d x}{x^{2}-\frac{\pi^{2}}{16}}\) is equal to :
- A \(f(2)\)
- B \(2 f(2)\)
- C \(2 f(\sqrt{2})\)
- D \(4 f(2)\)
Answer & Solution
Correct Answer
(B) \(2 f(2)\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \frac{\pi}{4}} \frac{\frac{\pi}{4} \int_{2}^{\sec ^{2} x} f(x) d x}{x^{2}-\frac{\pi^{2}}{16}}\) \(\lim _{x \rightarrow \frac{\pi}{4}} \frac{\pi}{4} \cdot \frac{\left[f\left(\sec ^{2} x\right) \cdot 2 \sec x \cdot \sec x \tan x\right]}{2 x}\)…
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