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Grade 12Integral Calculus

evaluate the following integral
∫ 1 / sqrt(1 – cos 2x) dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int \frac{1}{\sqrt{1-cos2x}}dx$
$I = \int \frac{1}{\sqrt{2sin^{2}x}}dx$
$I = \int \frac{1}{\sqrt{2}sinx}dx$
$I = \int \frac{cosecx}{\sqrt{2}}dx$
$I = \int \frac{cosecx(cosecx+cotx)}{\sqrt{2}(cosecx+cotx)}dx$
$cosecx+cotx = t$
$(-cosecxcotx-cot^{2}x)dx = dt$
$I = \int \frac{-1}{\sqrt{2}t}dt$
$I = \frac{-log(t)}{\sqrt{2}}$
$I = \frac{-log(cosecx+cotx)}{\sqrt{2}}$

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