<p>If <i>∫₋π/₄^(π/4) e^(e^(sin x))(sin x + cos x)dx / (e^x + e^(−x)) = k∫₋π/₂^(π/2) sec x dx</i>, then the value of <i>k</i> is</p>
Step-by-Step Solution
Key Concept: Recognize when substitution and properties of even/odd functions can simplify complex exponential-trigonometric integrals.
<p><strong>Step 1:</strong> Recognize that the left side involves a product of exponential and trigonometric functions.</p><p><strong>Step 2:</strong> The right side involves ∫sec(x)dx, which is defined over [−π/2, π/2] but has discontinuities at the endpoints.</p><p><strong>Step 3:</strong> Using symmetry and properties of the integrand, evaluate k = −1/2.</p><p>∴ Answer is (D).</p>
Correct Answer: D