इन समाकलनो का मान कीजिएः
`int_(0)^(1) (1)/(sqrt(1+x)-sqrt(x))dx`

Explanation

`underset(0)overset(1)int (1)/(sqrt(1+x)-sqrt(x))dx`
`=underset(0)overset(1)int((1)/(sqrt(1+x)-sqrtx)xx(sqrt(1+x)+sqrtx)/(sqrt(1+x)+sqrtx))dx`
`=underset(0)overset(1)int (sqrt(1+x)+sqrtx)/((1+x)-x)dx`
`=underset(0)overset(1)int (sqrt(1+x)+sqrtx)dx`
`=[2/3(1+x)^(3//2)-2/3x^(3//2)]_(0)^(1)`
`=[2/3(1+1)^(3//2)-2/3(1)^(3//2)] -[2/3(1+0)^(3//2)-2/3(0)^(3//2)]`
`=2/3(2)^(3//2)-2/3-2/3=2/3[2sqrt2-1-1]`
`=2/3(2sqrt2-2)=4/3(sqrt2-1)`