Integrals Flashcards
1
Q
What integration by parts?
A
-Integration by parts: ∫u dv/dx dx= ∫d(uv)/dx-∫v du/dx dx= uv-∫v du/dx dx
2
Q
How to do 2D integrals?
A
- Sketch the domain
- Find boundary conditions
3.Integrate over dy or dx
4.Integrate over dx or dy
2
Q
What are the spherical coordinates?
A
- Spherical coordinates
x=rsinθcosΦ
y=rsinθsinΦ
z=rcosθ
dV=r^2sinθdrdθdΦ
θ ranges from 0 to π
Φ ranges from 0 to 2π
2
Q
What are the 2D polar coordinates?
A
2D polar coordinates
x=rcosθ
y=rsinθ
dA=rdθdr
2
Q
What are the cylindrical coordinates?
A
- Cylindrical coordinates
x=rcosθ
y=rsinθ
z=z
dV=rdθdrdz
Here θ ranges from 0 to 2π
3
Q
What is the equation for a line integral?
A
=∫F(r).dl
Over a path C where l is parametrised
4
Q
What is a conservative field?
A
A field for which the line integral/ work done only depends on the start and end points
A field is conservative if P= ▽V
5
Q
What is the equation for a surface integral?
A
∫∫a.dS
