Calculus Volume 3 · free preview
Triple Integrals
Triple integrals accumulate over space regions as iterated integrals in three variables, computing volumes, masses, and averages, with the rectangular box the starting case and the general region's limits read from the solid.
1. Triple integrals over boxes
Triple integrals over boxes
2. General regions and limits
General regions and limits
3. Masses and averages
Masses and averages
4. The elemental setup pattern
The elemental setup pattern
5. Triple Riemann sum
A triple Riemann sum approximating the integral over a box sums which quantity?
6. Fubini three variables
Fubini's theorem for a continuous function on a box states which fact?
7. Volume as triple integral
The volume of a solid E equals which triple integral?
8. Average value three variables
The average value of f over E is which expression?
9. Order choice tactic
For a solid bounded by two surfaces over a plane region, which integration order is usually simplest?
10. Iterated count three variables
An iterated triple integral performs how many successive integrations? Answer with a number.
11. Unit cube volume
The triple integral of 1 over the unit cube equals what number? Answer with a number.
12. Center of mass denominator
The center of mass's coordinates divide the moment integrals by which quantity?
13. Mass integrand
A solid's mass is the triple integral of which quantity? Answer with one word.
14. Moment numerator
The center of mass's coordinates divide moments by the mass. As a single word, what does the moment integrate? Answer with the phrase mass times.
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