1. ## integration by parts

Hello Im still confused as to when i should change the limits. so far i have$\displaystyle \int_0^1 \arcsin(z)$ =$\displaystyle arcsin(z)\mbox{z}\$-$\displaystyle (1-z^2)$ with use of integration by parts and then substitution like if it were indefenit but do i have to change the limits or once i substitute back can i use the original limits to find the answer? Thank you

2. Hello,
Originally Posted by gabet16941
Hello Im still confused as to when i should change the limits. so far i have$\displaystyle \int_0^1 \arcsin(z)$ =$\displaystyle arcsin(z)\mbox{z}\$-$\displaystyle (1-z^2)$ with use of integration by parts and then substitution like if it were indefenit but do i have to change the limits or once i substitute back can i use the original limits to find the answer? Thank you
If you substitute back in the end, you don't need to change the limits.
If you don't substitute back, you have to change the limits as soon as you make the substitution.
And for further clearification, you can write $\displaystyle \int_{z=0}^{z=1}$. It would avoid careless mistakes

What you got should be corrected this way :

$\displaystyle \int \arcsin(z) ~dz=\arcsin(z) z-\sqrt{1-z^2}+C$

If you want to include the limits, let f(z) be the right hand side of the equation and the solution is $\displaystyle f(1)-f(0)$

3. Thank you! still trying to get use to the math input.. but I'm sure ill get there, thank you for the pointers.