The one with the log and trigonometry.

Calculus Level 5

Solve the following integral (upto 2 decimal places):

\[\displaystyle \large \int _{ 0 }^{ \pi /2 }{ \ln { ({ \sin }^{ 2 }x+{ k }^{ 2 }{ \cos }^{ 2 }x)dx } } \]

for \( k=12\)

Bonus: Generalize the integral for any value of \(k\)

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