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Grade 12Integral Calculus

evaluate the following integral
∫ sqrt{(1 – cos x) / (1 + cos x)} dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int \sqrt{\frac{1-cosx}{1+cosx}}dx$
$I = \int \sqrt{\frac{2sin^{2}\frac{x}{2}}{2cos^{2}\frac{x}{2}}}dx$
$I = \int \frac{sin\frac{x}{2}}{cos\frac{x}{2}}dx$
$cos\frac{x}{2}=t$
$-sin\frac{x}{2}\frac{dx}{2}=dt$
$I = -2\int \frac{dt}{t}$
$I = -2log(t)+c$
$I = -2log(cos\frac{x}{2})+c$
$I = 2log(sec\frac{x}{2})+c$

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