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Describe the three-dimensional region expressed in each iterated integral:

โˆซโˆ’24โ€Šโˆซ26โ€Šโˆซ05โ€Šf(x,y,z)dydxdz

Short Answer

Expert verified

โ„={(x,y,z)โˆฃ2โ‰คxโ‰ค6,0โ‰คyโ‰ค5,โˆ’2โ‰คzโ‰ค4}

Step by step solution

01

Step 1. Given information.

We have been given a three-dimensional region:

โˆซโˆ’24โ€Šโˆซ26โ€Šโˆซ05โ€Šf(x,y,z)dydxdz

We have to describe it in the iterated integral.

02

Step 2. Evaluate.

By the definition of triple integral โˆซa1a1โ€Šโˆซb1b2โ€Šโˆซc1c2โ€Šf(x,y,z)dzdydxrepresent the volume of the solid region โ„=(x,y,z)โˆฃa1โ‰คxโ‰คa2,b1โ‰คyโ‰คb2,c1โ‰คzโ‰คc2

The given triple integral represents the volume of the rectangular solid given byโ„={(x,y,z)โˆฃ2โ‰คxโ‰ค6,0โ‰คyโ‰ค5,โˆ’2โ‰คzโ‰ค4}

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