MATH 314 Study Guide - Final Guide: Mater Lectionis, String Vibration, Unit Cube

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 314
• Professor: Sidney Trudeau

Document Summary

Use a line integral to nd the plane area enclosed by the curve c: r = a cos3 t i + b sin3 t j (0 t 2 ). (cid:90) 2 (cid:90) 2 . Solution: we assume a > b > 0. (xy(cid:48) yx(cid:48))dt = 8 (sin4 t cos2 t + sin2 t cos4 t)dt. Compute the outward ux of the vector eld. Solution: let r be the region in r3 bounded by the surface s. we use the. We have divf = 3(x2 + y2 + z2), so that (cid:90) (cid:90) (cid:90) (cid:90) (cid:90) F ds = 3 (x2 + y2 + z2)dv := i. To compute the integral, we decompose the domain d into 2 regions: d = d1 d2, The integral i1 can be computed as follows: D1 = {(x, y, z) : 2 z 0, 0 x2 + y2 4},