- #1
jk22
- 729
- 24
When solving differential equations the following scripture can arise, for example:
$$\int \frac{df}{\sqrt{\sin(\theta)^2-f^2}}$$
If the change of variable ##f=\sin(\theta)\sin(u)##
Is performed, do the letters ##f,\theta## shall be considered independent or is
$$df=\cos(\theta)\sin(u)d\theta+\sin(\theta)\cos(u)du$$ ?
$$\int \frac{df}{\sqrt{\sin(\theta)^2-f^2}}$$
If the change of variable ##f=\sin(\theta)\sin(u)##
Is performed, do the letters ##f,\theta## shall be considered independent or is
$$df=\cos(\theta)\sin(u)d\theta+\sin(\theta)\cos(u)du$$ ?