Toronto Math Forum

MAT244--2018F => MAT244--Lectures & Home Assignments => Topic started by: Keanu Uchida on October 13, 2018, 05:12:29 PM

Title: Integral Methods for Test 1
Post by: Keanu Uchida on October 13, 2018, 05:12:29 PM
Which integrals from the 'integration methods' handout should we know from the test?

Are we supposed to know, say, how to integrate `Special Irrational Function II` that contains a root of a quadratic polynomial?
Title: Re: Integral Methods for Test 1
Post by: Victor Ivrii on October 13, 2018, 06:22:11 PM
All antiderivatives you are supposed to know
http://www.math.toronto.edu/courses/mat244h1/20189/LN/antiderivatives.pdf (http://www.math.toronto.edu/courses/mat244h1/20189/LN/antiderivatives.pdf)
Title: Re: Integral Methods for Test 1
Post by: Keanu Uchida on October 13, 2018, 08:07:49 PM
Well this is actually not what I'm asking. Obviously, we are expected to know these antiderivatives but I'm asking about integration methods that involve simplifying more complex functions into things that can be integrated more easily (with this table of antiderivatives).

For instance:
Which rational functions will we have to know to decompose before integrating?
We will be expected to evaluate trigonometric polynomials cos^m(x)sin^n(x) for n greater than 1? I think that the answer is yes and that is not information available on the antiderivative sheet.
Will we have to evaluate Trigonometric Rational Functions?

This is not answered on the sheet of antiderivatives.

Title: Re: Integral Methods for Test 1
Post by: Victor Ivrii on October 13, 2018, 08:48:16 PM
All rational functions for sure.

$\cos^m(x)\sin^n(x)$ for all $m\ge 0, n\ge0$.