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Chapter 13: Q. 7 (page 1054)

What is the difference between a triple integral and an iterated triple integral?

Short Answer

Expert verified

A triple integral is the limit of a Riemann sum over a rectangular solid $R$ as the limit of the mesh of subdivisions of $R$ goes to zero.

An iterated triple integral is the result of three consecutive integrations in the order specified by the placement of the variables of integration.

Step by step solution

01

Step 1. Given information

We need to write the difference between a triple integral and an iterated triple integral.

02

Step 2.The difference between a triple integral and an iterated triple integral:

A triple integral is the limit of a Riemann sum over a rectangular solid $R$ as the limit of the mesh of subdivisions of $R$ goes to zero.

An iterated triple integral is the result of three consecutive integrations in the order specified by the placement of the variables of integration.

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Most popular questions from this chapter

Evaluate each of the double integrals in Exercises 37–54 as iterated integrals.

$\int \int_{R} x \sin x \cos y d A, w h e r e R = {(x, y) | - 3 \leq x \leq 2 a n d - 2 \leq y \leq 2}$

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

$f (x, y) = \sin x \cos y W h e r e R = {(x, y) | 0 \leq x \leq π, 0 \leq y \leq π}$

Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.

$\int_{- 3}^{3} \int_{- \sqrt{9 - z^{2}}}^{\sqrt{9 - z^{2}}} \int_{0}^{3 - \sqrt{x^{2} + z^{2}}} f (x, y, z) d y d x d z$

Earlier in this section, we showed that we could use Fubini’s theorem to evaluate the integral $\int \int_{R} x^{2} y d A$ and we showed that $\int_{2}^{5} \int_{1}^{3} x^{2} y d x d y = 91$ Now evaluate the double integral by evaluating the iterated integral $\int_{1}^{3} \int_{2}^{5} x^{2} y d y d x$ .

Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.

$\int_{0}^{2} \int_{0}^{1 - 3 x / 2} \int_{2 x + (4 / 3) y - 4}^{0} f (x, y, z) d z d y d x$

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