Q. 47 - Calculus

Question

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

Exercise 37 with the order dx dy dz.

Step-by-Step Solution

Answer

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

${\int }_0^{3-y}{\int }_0^3{\int }_0^{3}f(x,y,z)dxdydz$

Step 1. Given Information.

We are given,

${\int }_0^3{\int }_0^3{\int }_0^{3-y}f(x,y,z)dzdydx$

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 $0 \text{to} 3$

The limit of y alters from $0 \text{to} 3$

The limit of z alters from $0 \text{to} 3-y$

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

${\int }_0^{3-y}{\int }_0^3{\int }_0^{3}f(x,y,z)dxdydz$