Chapter 1.5, Problem 1.48P

(a)

To determine

The value of the function $I={\displaystyle \int \left(r^2+r.a+a^2\right){\delta }^3\left(r-a\right)d\tau }$ .

(b)

To determine

The value of the function $I={\displaystyle \int {\left|r-b\right|}^2{\delta }^3\left(5r\right)d\tau }$ .

(c)

To determine

The value of the function $I={\displaystyle \int \left(r^4+r^2\left(r\cdot c\right)+c^4\right){\delta }^3\left(r-c\right)d\tau }$ .

(d)

To determine

The value of the function $I={\displaystyle \int \left(r\cdot \left(d-r\right)\right){\delta }^3\left(e-r\right)d\tau }$ .