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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 > 0

, if

I = \int \sqrt{\frac{x}{a^3 - x^3}} dx = A \sin^{-1} \left( \frac{x^{3/2}}{B} \right) + C

, where

C

is any arbitrary constant, then :

Options

A $A = \frac{2}{3}$
B $B = a^{3/2}$
C $A = \frac{1}{3}$
D $B = a^{1/2}$

Correct answer

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

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