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CBSE Class 12 · 2022 · Indefinite IntegralsShort Answer

Find

\int \frac{d x}{4 x - x ^{2}}

Answer: $sin^{- 1} (\frac{x - 2}{2}) + C$

Solution

Complete the square:

4 x - x^{2} = 4 - (x - 2)^{2} = 2^{2} - (x - 2)^{2}

. Then

\int \frac{d x}{2 ^{2} - ( x - 2 ) ^{2}} = sin^{- 1} (\frac{x - 2}{2}) + C .

sin^{- 1} (\frac{x - 2}{2}) + C

CBSE Class 12 Board · 2022 · Subjective

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