CRIM 101 Lecture 36: CRIM LEC36

し25-11 2)Using the substitutions-u and y=vu+v, evaluate y sin(y2 - z) dA where R is the region bounded by the curvestNx, x = 2, and y = 0.

y' - 2y = y-8 y8(dy/dt - 2y) = 1 V = y9 dv = 9y8 y8 dy / dt - 2y9 = 1 1 / 9 dv / dt = y8 dy / dt 1 / 9 dv / dt - 2v = 1 1 / 9 dv / dt - 18v / 9 = 1 dv / dt - 18V = 9 M(t) = eS18 dt = e18t Vu(t) = dt Vu(t) = = 1 / 2 e18 t + c V = e-18t (1 / 2 e18 t + c) = 1 / 2 + ce -18t y9 = 1 / 2 + ce -18t y = 9

Di , max/nun 1.25-11 2. Using the substitution u and y Vu+u, evaluate y sin(32-z) dA where R is the region bounded by the curves, 2, and y 0 2(sin(2)-2)