Area and volume integration Flashcards
What is the definition of the integral via a Riemann sum?
What does a single intergral find?
The area under a curve
What do double integrals find?
The volume under a surface
How can you define the double integral as the limit of the sum?
What is Fubini’s theorem.
What do we have to assume for Fubini’s theorem?
The area, A, is both vertically and horizontally simple.
What does vertically simple mean?
Each point inside A lies between exactly 2 points above/below it on boundary
What does horizontally simple mean?
Each point inside A lies between exactly 2 points left/right of it on boundary
How do you calculate the area in a plane between two curves?
What is the definition of a volume integral in terms of limits?
How do you calulcate the volume inside a surface?
