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CBSE Class 12 · 2011 · Indefinite IntegralsVery Short Answer

Write the value of

\int \frac{s e c ^{2} x}{cosec ^{2} x} d x

Answer: $tan x - x + C$

Solution

Rewrite the integrand using

sec^{2} x = \frac{1}{cos ^{2} x}

and

cosec^{2} x = \frac{1}{sin ^{2} x}

:

\frac{sec ^{2} x}{cosec ^{2} x} = \frac{sin ^{2} x}{cos ^{2} x} = tan^{2} x = sec^{2} x - 1.

Integrating,

\int (sec^{2} x - 1) d x = tan x - x + C

CBSE Class 12 Board · 2011 · Subjective

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