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Grade 12th passIntegral Calculus

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

udaybhansingh

11 Years agoGrade 12th pass

1 Answer

Jitender Singh

11 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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