Warm-up:

7.4 Trigonometric Substitutions

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.

We can use right triangles and the pythagorean theorem to simplify some problems. 1 These are in the same form.

We can use right triangles and the pythagorean theorem to simplify some problems. 1 These are in the same form.

We can use right triangles and the pythagorean theorem to simplify some problems. 1 This is a constant.

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.

2 double angle formula

2 double angle formula

5 We can get into the necessary form by completing the square.

6 Complete the square:

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

HW Day 1: p. 512 #’s 1-4, 5-17 odd, 41-45 odd

In Class/HW Day 2: p. 512 #’s 19-37 odd, 47, 49 odd