辅导案例-Z 2
1. [i] (Concept Checks): Determine whether the following statements are true or false. Circle your answer. • (True/False) Z 2 0 Z 1 0 xy2dydx = Z 2 0 xdx Z 1 0 y2dy. • (True/False) Z 4 1 x2 p ydy is a number. • (True/False) Z 1 0 Z x 0 f(x, y)dydx = Z 1 0 Z y 0 f(x, y)dxdy • (True/False) In polar coordinates, ZZ R drd✓ is the area of the closed and bounded region R. • (True/False) In cylindrical coordinates, ZZZ D rdrd✓dz is the volume of the solid D. • (True/False) Without calculating the integral, we can tell that Z R (x x2)dA where R = {(x, y) | 1 x 1 1 y 1} is negative. • (True/False) Z 1 0 Z 1 x dydx represents the area of a triangular region in the xy-plane. • (True/False) Given f(x, y) is a positive function and assuming the following integrals exist. We have Z 1 0 Z 1 0 f(x, y)dydx < Z 1 0 Z 1 x2 f(x, y)dydx < Z 1 0 Z 1 x3 f(x, y)dydx • (True/False) Z 3 0 Z 4x 0 f(x, y)dydx = Z 12 0 Z 3 y/4 f(x, y)dxdy. • (True/False) The region of the integration for Z r