Question

Trigonometric substitution,


Can you please help me out with the first one ? Just so that I can understand what to do.\
https://www.dropbox.com/s/qr65brhchm446fd/Screenshot%202013-10-26%2020.26.13.jpg

Answer 1

they completed the square, which would be necessary when solving these to put them in the proper form. of a^2 ± x^2

but for the first one u = x-1

Answer 2

"completed the square" what do you mean by that ?

Answer 3

The thing where you rewrite a quadratic like \(ax^2 + bx + c\) in the form \(a(x + b)^2 + c\)

Answer 4

Er, the b and the c aren't the same in those. But do you recognize it now.

Answer 5

\[\int{\frac{1}{\sqrt{x(x-2)+10}}}\]

Answer 6

The thing where you rewrite a quadratic like \(ax^2 + bx + c\) in the form \(a(x + d)^2 + e\)

There. :D

Answer 7

\[\int{\frac{1}{\sqrt{x(x-2)+10}}}\]


is that it ?

Answer 8

making a perfect square is quite a easy task.... just divide num. of x, add and subtract its square then.... then (x+ (coeff of x)with sign /2)^2 remaining is just addition and subtraction

Answer 9

so am I doing it right or what

Answer 10

wrong...

Answer 11

in first eqn coeff of x is -2, -2/2 = -1 (x^2-2x +1^2) -1^2 +10

Answer 12

are u okay wid it?

Answer 13

eqn coeff?

Answer 14

When rephrased coherently I think it says "In the first equation, the coefficient of x is -2, -2/2 = -1."
And then he explains how to complete the square. :D

Answer 15

my mistake... forgot to add comma :P

Answer 16

in first eqn,

Answer 17

ok what about that part ? -2/2 = -1

Answer 18

coeff of x/2

Answer 19

is there any x/2 in the exercise?

Answer 20

do you know the meaning of coefficient?

Answer 21

like if 2x coefficient of x is 2

Answer 22

yep..

Answer 23

?\

Answer 24

What part are you getting stuck on Christos? :O
The completing the square stuff?

Answer 25

i said yes... :D u did that gud

Answer 26

yes @ZeHanz thats where I stuck

Answer 27

It looks like they did the `completing the square` for you, and they're asking you what substitution you should make.

In part a) \(\Large u\quad=\quad 3\tan\theta\)

Answer 28

But as Euler stated, maybe they want to know how you got from x to u.
I'm a little confused on the wording of the question :(