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!
Hello, margaritas,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
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.