Problem with definate integrals?

[twohaha]

First make a substitution and then use integration by parts to evaluate the integral:

[tex]\int[/tex] sin (sqrt x)dx

This is what I have done up to now:

dv = dx
v = x
sin (sqrt x) = u
(0.5 cos (sqrt x))/ sqrt (x) = du

x sin (sqrt x) - [tex]\int[/tex] (0.5x cos (sqrt x))/ sqrt (x)dx

[Subhotosh Khan]

First make a substitution and then use integration by parts to evaluate the integral:

[tex]\int[/tex] sin (sqrt x)dx

This is what I have done up to now:

dv = dx
v = x
sin (sqrt x) = u
(0.5 cos (sqrt x))/ sqrt (x) = du

x sin (sqrt x) - [tex]\int[/tex] (0.5x cos (sqrt x))/ sqrt (x)dx

[tex]\int[/tex] sin (sqrt x)dx

substitute

u = √x → u² = x → dx = 2u du

[tex]\int[/tex] sin (sqrt x)dx = 2[tex]\int[/tex] u * sin (u)du

Now use integration by parts.......