Question

When can you use trigonometric substitution in Integral Calculus?

Answer 1

When it is necessary.

Answer 2

does it need to be inside a radical?

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcII/TrigSubstitutions.aspx

Answer 4

for example:

can you use it here?

dx/(9 - x^2)

Answer 5

This one you do it by partial fractions

Answer 6

why can't you use trigonometric substitution?

Answer 7

it follows a^2 - u^2

Answer 8

\[
\frac{1}{9-x^2}=\frac{1}{6
(x+3)}-\frac{1}{6 (x-3)}
\]

Answer 9

if you put x =3 sin(t), dx
3 cos(t)dt
How do you continue?

Answer 10

\[
\frac{1}{9-x^2}=\frac{1}{6
(x+3)}-\frac{1}{6 (x-3)}
\]

I can't see what you've written properly

Answer 11

Yes that is it

Answer 12

http://www.wolframalpha.com/input/?i=1%2F%289-x^2%29

Answer 13

Do you see now?

Answer 14

http://www.wolframalpha.com/input/?i=integral+1%2F%289-x^2%29

Answer 15

yes, thanks
To answer your question, I will substitute 3 sin(t) to x
and 3 cos(t)dt to dx.

Answer 16

But you end up having to integrate sec(x), I think you can do it this way.

Answer 17

The usual way to your problem is by partial fraction.

Answer 18

I actually got up the sec (x) part.
Yes, I know that it can be solved by partial fractions, can you also use trig substitution.

Because I am confused if you only use trig substitution if the form is:
sqrt(a^2 - u^2)
sqrt(a^2 + u^2)
sqrt(u^2 - a^2)

or you can do it as long as it is in the form:

a^2 - u^2
a^2 + u^2
u^2 - a^2

whatever power it is raised, For example:
(a^2 - u^2)^2

Please help me :)

Answer 19

@eliassaab hey

Answer 20

anyone?

Answer 21

I'm just confused because the books shows it in radicals (raised to 1/2)
but my teacher used in non-radicals (raised to 2)

Answer 22

I hope someone can enlighten me. :)

Answer 23

There are always more than one way to do a particular math problem.
The beauty in math is to chose the easiest way to do it.
If you plan to go from Chicago to Seattle, you can go straight or you can fly to NY and then back to Seattle. Both ways will get you to Seattle, but takes 8 hours less to get there.
Chose the fast and easy one.

Answer 24

so does it mean I can use trig substitution? I'm just trying to understand the concept in trig substitution. :)

Answer 25

@moongazer
Can you post whatever part of your question you still don't understand ??

Answer 26

@LastDayWork

I am confused if you can only use trig substitution if the form is:
sqrt(a^2 - u^2)
sqrt(a^2 + u^2)
sqrt(u^2 - a^2)

or you can do it as long as it is in the form:

a^2 - u^2
a^2 + u^2
u^2 - a^2

whatever power it is raised, For example:
(a^2 - u^2)^2

Answer 27

u is the variable of integration, right ??

Answer 28

"sqrt(a^2 - u^2)
sqrt(a^2 + u^2)
sqrt(u^2 - a^2) "

Most people remember their formulas..it can be solved by integration by parts.
And by my (limited) experience; the question which require "by parts" can't be solved by substitution.

Answer 29

Yes?, it is a function
du

Answer 30

In general, you have to do a hit and trial when it comes to substitution..but there are some formats which literally shout for trig substitutions..

Answer 31

So you can use it even though it is not inside a square root?

Answer 32

You can use it whenever you can completely substitute the previous variable..

I am trying to find some standard tricks on google..don't wanna type them all myself XD

Answer 33

Thanks to both of you for the help.
That's the answer iv'e been looking. :)

Answer 34

:)

Answer 35

Just for clarification, so the square root doesn't matter?
My book and other reference only shows it (with square root) because it is commonly used in that form?