Definite Integrals

₀âˆ«^Ï€/3 cos x/(3+4 sin x)dx = k log(3 + 2âˆš3/3)..

the value of k =

A. 1/2
B. 1/3
C. 1/4
D. 1/5

1 Answers

106

Asish Mahapatra ·2009-10-01 22:56:51

d(3+4sinx) = 4cosxdx

So, taking 3+4sinx as t, we get the integral as

âˆ«dt/4t (t from 3 to t=3+2âˆš3)

= [14log(t)]

evaluating limits,

= 14log3+2âˆš33

So K = 1/4

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