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Definite Integration question

2015 · Shift 2 · Q35

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2015 · Shift 2 · Q35

Definite Integration question

2015 · Shift 2 · Q35

JEE AdvancedMathematicsDefinite IntegrationMultiple correct+4 / −1

The option(s) with the values of a and

L

that satisfy the following equation is (are)

{{\int\limits_0^{4\pi } {{e^t}\left( {{{\sin }^6}at + {{\cos }^4}at} \right)dt} } \over {\int\limits_0^\pi {{e^t}\left( {{{\sin }^6}at + {{\cos }^4}at} \right)dt} }} = L?

A
$a = 2,L = {{{e^{4\pi }} - 1} \over {{e^\pi } - 1}}$
B
$a = 2,L = {{{e^{4\pi }} + 1} \over {{e^\pi } + 1}}$
C
$a = 4,L = {{{e^{4\pi }} - 1} \over {{e^\pi } - 1}}$
D
$a = 4,L = {{{e^{4\pi }} + 1} \over {{e^\pi } + 1}}$

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