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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

For a > 0 , if I = ∫ (x)/(a^3 - x^3) dx = A ^ -1 ( x^ 3/2 B ) + C ,...

For a>0a > 0, if I=∫xa3−x3dx=Asin⁡−1(x3/2B)+CI = \int \sqrt{\frac{x}{a^3 - x^3}} dx = A \sin^{-1} \left( \frac{x^{3/2}}{B} \right) + C, where CC is any arbitrary constant, then :

Options

  1. AA=23A = \frac{2}{3}
  2. BB=a3/2B = a^{3/2}
  3. CA=13A = \frac{1}{3}
  4. DB=a1/2B = a^{1/2}

Correct answer

A. A=23A = \frac{2}{3}

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