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Solved: Integrals over boxes Evaluate the following
Chapter 12, Problem 12E(choose chapter or problem)
Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be useful.
\(\int_{0}^{2} \int_{1}^{2} \int_{0}^{1} y z e^{x} \ d x \ d z \ d y\)
Questions & Answers
QUESTION:
Integrals over boxes Evaluate the following integrals. A sketch of the region of integration may be useful.
\(\int_{0}^{2} \int_{1}^{2} \int_{0}^{1} y z e^{x} \ d x \ d z \ d y\)
ANSWER:Solution 12E
(yz
)dx dy dz
Let F=(yz)
This is definite integral problem with three variable of a function
Step 1:
First Integrate the function F with respect to dx with limit 0 to 1
yz
dx=
( compute the definite integral with limit 0 to 1)
=(yz ) since (
=e,
=1)
= yz(e-1)