हल कीजिए-
`(dy)/(dx)=sin ^(-1)x.`

Explanation

`(dy)/(dx)=sin^(-1)x`
`impliesdy =sin ^(-1)xdx`
समाकलन करने पर,
`intdy =intsin ^(-1)xdx`
`implies int dy =int underset(II)I underset(I)sin ^(-1)x dx`
`impliesy=x. sin ^(-1)x-int{(d)/(dx)(sin ^(-1)x). int 1 dx}dx`
`implies y=x sin ^(-1) x-int(x)/(sqrt(x-x^(2))dx`
माना `1-x^(2)=timplies -2 xdx =dt impliesxdx =-(dt)/(2)`
`therefore y=x sin ^(-1)x+1/2 int (dt)/(sqrtt)`
`impliesy=x sin ^(-1)x+(1)/(2)(t^(1//2))/(2(1//2))+C`
`impliesy=x sin ^(-1)x+sqrt(1-x^(2))+C, [becauset=1-x^(2)]`