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evaluate integration 0 to pi by 3 step function of root 3 tanx dx

evaluate integration 0 to pi by 3 step function of root 3 tanx dx

Grade:12th pass

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int_{0}^{\pi /3}\sqrt{3}tanxdx
I = \int_{0}^{\pi /3}\sqrt{3}\frac{sinx}{cosx}dx
cosx = t
-sinxdx = dt
x = 0\rightarrow t = 1
x = \pi /3\rightarrow t = 1/2
I = \int_{1/2}^{1}\sqrt{3}\frac{1}{t}dt
I = \sqrt{3}ln(t)_{1/2}^{1}
I = \sqrt{3}ln(2)

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