=∫∫∫_V dV
This is a sphere, so use spherical coordinates.
=∫& lt; 0,2π& gt; ∫& lt; 0,π& gt; ∫& lt; 0,r & gtρ^2 sin φ dρdφdθ
=∫& lt; 0,2π& gt; dθ∫& lt; 0,π& gt; sinφdφ∫& lt; 0,r & gtρ^2dρ
= 2π*[-cosφ| & lt; 0,π& gt; ]*[ρ^3/3 | & lt; 0,r & gt]
=2π*2*r^3/3
=4πr^3/3
I hope I can help you. This is a triple integral.