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If int(0)^(4pi)ln|13sinx+3sqrt3cosx|dx=k...

If `int_(0)^(4pi)ln|13sinx+3sqrt3cosx|dx=kpiln7`, then the value of k is

A

2

B

4

C

8

D

16

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(0)^(4pi)ln|13sinx+3sqrt3cosx|dx`
`=4int_(0)^(4pi)ln|14sin(x+tan^(-1).(3sqrt3)/(13))|dx`
`=8int_(0)^(pi//2)(ln14+log|sinx|)dx`
`=4pi(ln14-ln2)=4piln7.`
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