1. Problem with definate integrals?

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

$\int$ 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) - $\int$ (0.5x cos (sqrt x))/ sqrt (x)dx

2. Originally Posted by twohaha
First make a substitution and then use integration by parts to evaluate the integral:

$\int$ 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) - $\int$ (0.5x cos (sqrt x))/ sqrt (x)dx
$\int$ sin (sqrt x)dx

substitute

u = √x → u2 = x → dx = 2u du

$\int$ sin (sqrt x)dx = 2$\int$ u * sin (u)du

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

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