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GUJCET · Maths · Application of Derivatives
\(\int \frac{d x}{\sqrt{4 x-9 x^2}}=\) ___________ + C
- A \(\frac{1}{3} \sin ^{-1}\left(\frac{9 x-2}{2}\right)\)
- B \(\frac{1}{9} \sin ^{-1}\left(\frac{3 x-2}{2}\right)\)
- C \(\frac{1}{9} \sin ^{-1}\left(\frac{2 x-3}{3}\right)\)
- D \(\frac{1}{2} \sin ^{-1}\left(\frac{9 x-3}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3} \sin ^{-1}\left(\frac{9 x-2}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(\int \frac{d x}{\sqrt{4 x-9 x^2}} = \int \frac{d x}{\sqrt{-(9x^2 - 4x)}}\) \( = \int \frac{d x}{\sqrt{-9(x^2 - \frac{4}{9}x)}}\)
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