MATB41H3 Lecture 22: MATB41 Week 11
Document Summary
We consider 2 practical approaches to computing the triple integral. Zb f dv = zzz b f dv. Fix one variable, say (w. l. o. g. ) z and let rz be the planar region consisting of the points in b with z xed (the cross section). Then zb f dv = z (cid:18)zz rz f da(cid:19) dz. We now compute the double integral over rz as a function of z and then integrate w. r. t. z. Fix two variable, say (w. l. o. g. ) x and y, and integrate out the third variable, z, leaving a function of two variables. We then integrate this function of two variables over the projection of b into the xy plane. Hence zb f dv = zz xy proj (cid:18)z f dz(cid:19) da. The rst octant region bounded by z = 1 x2 and y = x (with the face in the xz plane removed).
