Question: Using the substitution x = 1/y, or otherwise, find: (see attached)

Sorry for the picture quality, I took it off my phone.

It's x and in the bracket, x^2 you see there.

Thanks in advance!

Printable View

- Jul 26th 2006, 12:10 AMmargaritasAnother integration question!
Question: Using the substitution x = 1/y, or otherwise, find: (see attached)

Sorry for the picture quality, I took it off my phone.

It's x and in the bracket, x^2 you see there.

Thanks in advance! - Jul 26th 2006, 12:29 AMearbothQuote:

Originally Posted by**margaritas**

do you mean:

If so the result is

Steps to reach this result will follow.

Greetings

EB - Jul 26th 2006, 12:54 AMmargaritas
Thanks for the help, EB, yep that's the question. But the answer as given by my tutor is supposedly: C - sin^(-1) (1/x).

- Jul 26th 2006, 10:27 AMearbothQuote:

Originally Posted by**margaritas**

it's me again.

As you suggested, use . So .

Substitute the x and the dx and you'll get:

. Rearrange:

=

As you may see, this is

So the answer given in your book is OK - but my result is true too. There are integrals with different solutions. After a few steps of transformation, you'll reach my result. Have a look here:

http://www.mathhelpforum.com/math-he...ead.php?t=4278

Greetings

EB - Jul 27th 2006, 06:24 AMSoroban
Great work, EB!

It seems to invite Trig Substitution,

. . so I tried it . . . and found yet another solution.

Let

Substitute: .

Back-substitute: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Our three answers are equivalent.

I had:

is an angle is a right triangle with:Code:`*`

x * | ______

* | √x² - 1

* θ |

* - - - - - *

1

Your answer . .is the same angle.

The other acute angle is: . and

Hence: .

. . which verifies margaritas' solution.

- Jul 29th 2006, 04:52 AMmargaritas
Thanks for the help, guys! :)