For \( a0 \), if \( I=\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=A \sin ^{-1}\left(\frac{x^{3 / 2}}{B...
For \( a0 \), if \( I=\int \sqrt{\frac{x}{a^{3}-x^{3}}} d x=A \sin ^{-1}\left(\frac{x^{3 / 2}}{B}\right)+C \), where \( C \) is any arbitrary constant, then :
(a) \( A=\frac{2}{3} \)
(b) \( B=a^{3 / 2} \)
(c) \( A=\frac{1}{3} \)
(d) \( B=a^{1 / 2} \)
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