Thomas’ Calculus Early Transcendentals 12ed

Study Guide for Chap 15

1. Study how to identify the limits of integration ∫_{∗}^{∗} ∫_{∗}^{∗} dxdy and ∫_{∗}^{∗} ∫_{∗}^{∗} dydx for general domains (that is, not rectangles).

2. Study how to interchange between ∫ ∫ dxdy and ∫ ∫ dydx for general domains as in problems 33-54 of section 15.2.

3. Study why dA = rdrdθ in polar coordinates and how to determine the limits of integrations in ∫_{∗}^{∗} ∫_{∗}^{∗}(∗)rdrdθ as in examples 2-6 in section 15.4.