Multiple Integrals

Lesson · Advanced

Calculus

Area and Volume by Integrals

A=R1dAA=\iint_R 1\,dA
V=D1dVV=\iiint_D 1\,dV

Choosing Limits of Integration

f(x,y,z)dzdydx\iiint f(x,y,z)\,dz\,dy\,dx

Choose the limits from inside to outside.

z=z(x,y),y=y(x),x=constantz=z(x,y),\qquad y=y(x),\qquad x=\text{constant}