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Home Multiple Integrals Triple Integrals Examples Example 1
 
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Example 1

Evaluate 12_multiple_integrals-328.gif where E is the rectangular box

0 ≤ x ≤ 2, 0 ≤ y ≤ 1, 0 ≤ z ≤ 4.

There are six iterated integrals which all have the same value. We compute one of them, and then another to check our answer.

FIRST SOLUTION

12_multiple_integrals-329.gif

The inside integral is

12_multiple_integrals-330.gif

The second integral is

12_multiple_integrals-331.gif

The final answer is

12_multiple_integrals-332.gif

SECOND SOLUTION

12_multiple_integrals-333.gif

The inside integral is

12_multiple_integrals-334.gif

The second integral is

12_multiple_integrals-335.gif

The final answer is

12_multiple_integrals-336.gif

Triple integrals can be evaluated by iterated integrals.
Home Multiple Integrals Triple Integrals Examples Example 1

Last Update: 2006-11-15