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CBSE Class 12 · 2011 · Definite IntegralsVery Short Answer

Write the value of

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

Answer: $lo g 2$

Solution

The numerator is the derivative of the denominator, so the integral is a logarithm:

\int_{0}^{1} \frac{2 x}{1 + x ^{2}} d x = [lo g (1 + x^{2})]_{0}^{1} = lo g 2 - lo g 1 = lo g 2

CBSE Class 12 Board · 2011 · Subjective

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