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CBSE Class 12 · 2011 · Definite IntegralsVery Short Answer

Evaluate :

\int_{0}^{1} \frac{d x}{1 - x ^{2}}

Answer: $\frac{π}{2}$

Solution

An antiderivative of

\frac{1}{1 - x ^{2}}

is

sin^{- 1} x

. By the Fundamental Theorem of Calculus,

\int_{0}^{1} \frac{d x}{1 - x ^{2}} = [sin^{- 1} x]_{0}^{1} = sin^{- 1} 1 - sin^{- 1} 0 = \frac{π}{2} - 0.

\frac{π}{2}

CBSE Class 12 Board · 2011 · Subjective

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