JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int {{e^{\sec \,x}}\,\left( {\sec \,x + \tan \,x\,f\left( x \right) + \left( {\sec \,x\,\tan \,x + {{\sec }^2}\,x} \right)} \right)dx = {e^{\sec \,x\,}}\,f\left( x \right)} + C\) , then a possible choice of \(f\left( x \right)\) is
- A \(\sec \,x - \tan \,x - \frac{1}{2}\)
- B \(x\,\sec \,x + \tan \,x + \frac{1}{2}\)
- C \(\,\sec \,x + x\,\tan \,x - \frac{1}{2}\)
- D \(\,\sec \,x + \tan \,x + \frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\,\sec \,x + \tan \,x + \frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\int e^{\sec x}\left(\sec x+\tan x f(x)+\left(\sec x \tan x+\sec ^{2} x\right)\right) d x\) \(=e^{\sec x} f(x)+C\) Diff. both side w.r.t. \(x\) \(=e^{\sec x}\left(\sec x+\tan x+f(x)+\left(\sec x \tan x+\sec ^{2} x\right)\right)\)…
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