definite Integral.. (1may)

\hspace{-16}\bf{\int_{0}^{4\pi}\ln\left|13.\sin (x)+3\sqrt{3}.\cos (x)\right|dx}=

3 Answers

262
Aditya Bhutra ·

ANs : 2Ï€.ln(7/2)

71
Vivek @ Born this Way ·

Aditya, How did you do it? I'm getting stuck at this integral : 0 ∫ ln(sin (x+a)) dx , a ε C

262
Aditya Bhutra ·

since sin(x-a) is a periodic function ,

0∫4pi f ( sin(x-a)) = 0-a∫4pi-a f( sin (x-a))

then x-a =t

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