Question # The value of ( n ) is

# The value of ( n ) is

(a) 0

(b) -1

( (c) 1 )

(d) none of these

Solution

( int frac{d x}{sqrt{2 a x-x^{2}}}=int frac{d x}{sqrt{a^{2}-left(x^{2}-2 a x+a^{2}right)}} )

( =int frac{d x}{sqrt{a^{2}-(x-a)^{2}}} sin ^{-1}left(frac{x-a}{a}right)=sin ^{-1}left(frac{x}{a}-1right) )

( =sin ^{-1}left(frac{x}{a}-1right)=a^{n} sin ^{-1}left(frac{x}{a}-1right) )

( Rightarrow {a^{n}=1}) ({n=0} ) Option (a)