Integration of d(xyz)

Answer 1

Start by calculating the derivative of xyz with respect to x.

d(xyz)/dx = yz ; y, z treated as constants

d(xyz) = yz dx ; multiply both sides by dx

∫d(xyz) = ∫yz dx ; integrate both sides

= yz ∫dx

= yzx = xyz

Alternatively, if x, y and z are functions of t. You can use the product rule to see that

d(xyz)/dt = xy * dz/dt + xz * dy/dt + yz * dx/dt

d(xyz) = xy*dz + xz*dy + yz*dx ; multiplying both sides by dt

∫d(xyz) = ∫xy*dz + ∫xz*dy + ∫yz*dx ; integrating both sides