Q. 45 - Calculus

Question

In Exercises 45–52, rewrite the indicated integral with the specified order of integration. 

Exercise 35 with the order dx dy dz.

Step-by-Step Solution

Answer

The given indicated integral with the specified order of integration is,

${\int }_{-2}^4{\int }_0^5{\int }_2^{6}f(x,y,z)dxdydz$

Step 1. Given Information.

We are given,

${\int }_{-2}^4{\int }_2^6{\int }_0^{5}f(x,y,z)dydxdz$

Step 2. Rewriting the integral.

We have to write the given integral in order of dx dy dz .

So, the limit of the integration will vary as follows:

The limit of x  alters from $2 \text{to} 6$

The limit of y alters from $0 \text{to} 5$

The limit of z alters from $-2 \text{to} 4$

Hence the indicated integral with the specified order of integration is,

${\int }_{-2}^4{\int }_0^5{\int }_2^{6}f(x,y,z)dxdydz$