6.4 Trigonometric Substitution

Question 1

square root of a^2 - x^2

Answer 1

x = a sin theta

Question 2

square root of x^2 + a^2

Answer 2

x = a tan theta

Question 3

square root of x^2 - a^2

Answer 3

x = a sec theta

Question 4

How to solve a problem with trigonometric substitution when it is a definite integral

Answer 4

1. find a (square root of number you see)
2. find x based on trig you see
3. find dx
4. change bounds
5. plug in x and dx
6. simplify with trig identity
7. simplify carefully showing each step if needed
8. solve a 6.3 problem

Question 5

how to solve a indefinite integral with trigonometric substitution

Answer 5

1. find a (square root of number you see)
2. find x based on the trig you see
3. find dx
4. convert to theta by plugging in x and dx
5. simplify
6. use a trig identity
7. 6.3 problem
8. go back to original variable with some trig knowledge and info you have

Question 6

if after you have plugged in x and dx with theta and you still have an x what do you do?

Answer 6

change to theta with what x equals at the beginning of solving…step 2

Question 7

do you need to see the square root to use this type of substitution

Answer 7

no just need one variable alone squared with a constant
skip steps 1, 2, 3,
just directly plug in the substitution into the variable squared and constant squared
- problem 4 on hw

Question 8

if you are given an equation that does not look like you can use this substitution(say a polynomial) …how do you make it look like it

Answer 8

goal is to get a variable squared
- complete the square
- use u-sub to use u as your variable