Step 1

Given: The integrand of a triple integral involves \(x^{2} + y^{2}\)

Step 2

Explanation:

A cylindrical coordinate system is used in triple integrals only.

Therefore, it is cylindrical coordinate system

Because \(x = r \cos (\theta), y = r \sin (\theta)\ and\ z = z\)

So, \(x^{2} +y^{2} = r^{2}\)

z axis is same in both systems.

So, The integrand of a triple integral involves \(x^{2} + y^{2}\) then its suggested to use cylindrical coordinate system

Given: The integrand of a triple integral involves \(x^{2} + y^{2}\)

Step 2

Explanation:

A cylindrical coordinate system is used in triple integrals only.

Therefore, it is cylindrical coordinate system

Because \(x = r \cos (\theta), y = r \sin (\theta)\ and\ z = z\)

So, \(x^{2} +y^{2} = r^{2}\)

z axis is same in both systems.

So, The integrand of a triple integral involves \(x^{2} + y^{2}\) then its suggested to use cylindrical coordinate system