Download presentation
1
Warm-up:
2
7.4 Trigonometric Substitutions
4
Integrals involving Inverse Trig Functions
When listing the Antiderivative that corresponds to each of the inverse trigonometric functions, only use one member from each pair. a is the number. u is the variable.
5
We can use right triangles and the pythagorean theorem to simplify some problems.
1 These are in the same form.
6
We can use right triangles and the pythagorean theorem to simplify some problems.
1 These are in the same form.
7
We can use right triangles and the pythagorean theorem to simplify some problems.
1 This is a constant.
8
This method is called Trigonometric Substitution.
If the integral contains , we use the triangle at right. If we need , we move a to the hypotenuse. If we need , we move x to the hypotenuse.
9
2 double angle formula
10
2 double angle formula
11
5 We can get into the necessary form by completing the square.
12
6 Complete the square:
13
Here are a couple of shortcuts that are result from Trigonometric Substitution:
These are on your list of formulas. They are not really new. p
14
HW Day 1: p. 512 #’s 1-4, 5-17 odd, odd
15
In Class/HW Day 2: p. 512 #’s 19-37 odd, 47, 49 odd
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.