formulas for the math chapter 15

Question 1

What is the formula for dV in spherical coordinates?

Answer 1

dV=ρ²*sinΦdρdΦdΘ

Question 2

What is the formula for dV in cylindircal coordinates?

Answer 2

dV=r*dz*dr*dΘ

Question 3

What is the formula for dA in polar coordinates?

Answer 3

dA=r*dr*dΘ

Question 4

what is formula for dV in rectangular coorindates?

Answer 4

dV=dz*dy*dx

Question 5

analyze what each components of triple integral do with respect to shadow

Answer 5

the dy and dz will define our darn shadow and and the first two sigma signs define shadow and the triple integral as a whole will define the damn 3d region.

Question 6

what can (sin(Θ))² expand to?

Answer 6

Question 7

What can (cos(Θ))² expand to?

Answer 7