MATH 1004 Lecture Notes - Lecture 10: Polynomial, Product Rule, Trigonometric Functions

• School: Carleton University
• Department: Mathematics
• Course: MATH 1004
• Professor: Glenn Mc Rae

Document Summary

7. 3 integration by parts: reverse operation according to product rule. Example: evaluate(cid:82) x sin xdx udv = uv : the table method. This is a more rapid way of setting up the integration by part environment. (cid:90) u dv dx dx. Look at every row of the table and see if any of the products of the two quantities in the row can be integrated without much e ort. If you nd such a row or see zero in the left column, stop lling in the table. Let"s say you decide to stop at row n . Then the last term in your answer must be the integral of the product of the two functions in that row by the constant ( 1)n 1. For example, you want to stop in row 4: dx = u(x)v(x) u(cid:48)(x)v(1)(x) + u(cid:48)(cid:48)(x)v(2)(x) u(cid:48)(cid:48)(cid:48)(x)v(3)(x) + u(4)(x)v(3)(x)dx (cid:90) (cid:90) u dv dx.