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Integral Calculus> Integrate from (pi)/6 to (pi)/3 ∫dx/(1+ta...

question mark

Integrate from (pi)/6 to (pi)/3
∫dx/(1+tan⁵x)

Lovey , 11 Years ago

Grade 12

2 Answers

Jitender Singh

Last Activity: 11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int_{\pi /6}^{\pi /3}\frac{1}{tan^{5}x + 1}dx$ …......(1)
$I = \int_{\pi /6}^{\pi /3}\frac{1}{tan^{5}(\frac{\pi }{2}-x) + 1}dx$
$I = \int_{\pi /6}^{\pi /3}\frac{1}{cot^{5}x + 1}dx$
$I = \int_{\pi /6}^{\pi /3}\frac{tan^{5}x}{tan^{5}x+1}dx$ ….......(2)
(1) + (2)
$2I = \int_{\pi /6}^{\pi /3}\frac{1+tan^{5}x}{tan^{5}x+1}dx$
$2I = \int_{\pi /6}^{\pi /3}1.dx$
$2I =[x]_{\pi /6}^{\pi /3}$
$2I =\frac{\pi }{3} - \frac{\pi }{6}$
$2I =\frac{\pi }{6}$
$I =\frac{\pi }{12}$

Lovey

Last Activity: 11 Years ago

Thanx.

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