Hello everybody!
I am trying to differentiate a function defined as:
J1 = \int_{-beta(r)}^{beta(r)} \int_{X_m(b,r)}^{X_x(b,r)} z*P(z)*ind(z<x) dz db
where:
"ind" is the indicator function ;
beta(r) = asin(r/R) ;
-beta(r) < b < beta(r) ;
X_x(b,r) = R cos(b) + sqrt{r^2-(R sin(b))^2} ;
X_m(b,r) = R cos(b) - sqrt{r^2-(R sin(b))^2} .
Actually I tried to apply Liebniz rule but the problem is how to differentiate the indicator function.
Thanks in advance for your help!
I am trying to differentiate a function defined as:
J1 = \int_{-beta(r)}^{beta(r)} \int_{X_m(b,r)}^{X_x(b,r)} z*P(z)*ind(z<x) dz db
where:
"ind" is the indicator function ;
beta(r) = asin(r/R) ;
-beta(r) < b < beta(r) ;
X_x(b,r) = R cos(b) + sqrt{r^2-(R sin(b))^2} ;
X_m(b,r) = R cos(b) - sqrt{r^2-(R sin(b))^2} .
Actually I tried to apply Liebniz rule but the problem is how to differentiate the indicator function.
Thanks in advance for your help!