Evaluate the following integrals: (a) f all space (r2 + r a + a2) 3 (r

Evaluate the following integrals:

(a) f all space (r2 + r ∙ a + a2) δ3 (r – a) dτ, where a is a fixed vector and a is its magnitude.

(b) fv | r – b|2 δ3 (5r) dr, where V is a cube of side 2, centered on the origin, and b = 4y + 3z.

(c) fv (r4 + r2(r ∙ c) + c4) δ3 (r – c) dτ, where V is a sphere of radius 6 about the origin, c = 5 x + 3y + 2z, and c is its magnitude.

(d) fv r ∙ (d – r) δ3 (e – r) dτ, where d = (1, 2, 3), e = (3, 2, 1), and V is a sphere of radius 1.5 centered at (2, 2, 2).