Definite Integration
Trigonometric Integrals
Grade 12
Question:
<p>The value of <span>\(\int_0^{\pi/2} \ln(\sin^2\theta + k^2\cos^2\theta) d\theta\)</span> is equal to</p>
<p>(A) \(\ln(1+k) - \ln 2\)</p>
<p>(B) \(\ln 2 - \ln(1+k)\)</p>
<p>(C) \(\ln(1+k) - \ln 2\)</p>
<p>(D) none of these</p>
Step-by-Step Solution
Key Concept: Use logarithm properties and definite integral substitution techniques to evaluate the integral.
<p>This is an indefinite integral problem requiring substitution and properties of logarithmic integrals.</p>
Correct Answer: A