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Definite Integration question

2023 · 1 Feb · Shift 2 · Q41

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 1 Feb · Shift 2 · Q41

Definite Integration question

2023 · 1 Feb · Shift 2 · Q41

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If

\int\limits_0^\pi {{{{5^{\cos x}}(1 + \cos x\cos 3x + {{\cos }^2}x + {{\cos }^3}x\cos 3x)dx} \over {1 + {5^{\cos x}}}} = {{k\pi } \over {16}}}

, then k is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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