1.

If `intsqrt((x)/(a^(3)-x^(3)))dx=msin^(-1)((x)/(a))^(n)+C`, thenA. m = nB. m =-nC. `m=1//n`D. `m=-1//n`

Answer» Correct Answer - c
We have , `I=intsqrt((x)/(a^(3)-x^(3)))dx = int(sqrt(x))/(sqrt((a^(3//2))^(2)-(x^(3//2))^(2))dx`
`rArr I=(2)/(3)int(1)/(sqrt((a^(3//2))^(2)-(x^(3//2))^(2)))d (x^(3//2))`
`rArrI=(2)/(3)sin^(-1)((x)/(a))^(3//2)+C`
`:. m = (2)/(3)andn=(3)/(2) rArr m = (1)/(n)`


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