studip question (1 Viewer)

[ToO LaZy ^*]

int (1 / sqrt(1 - 4(x)^2) ) dx
= 1/2 * sin^-1(2x) + C for some constant

one thing i don't understand is why there is a half outside of sin (the bit in the bold) coz in the standard integrals table it only says sin^-1 (x/a) ...?

 

[Teoh]

Because for the sin^-1 integral
You need d/dx in the numerator (2), so you need to take a half outside in order to balance...

 

[ToO LaZy ^*]

umm..hmm..ok.kinda get it..thx tho

 

[J0n]

The thing is, the standard integral is for int (1 / sqrt(a² - x²) ) - with no coefficient in front of x (just 1) .'. you have to make your integral like that (let u = 2x)

 

[:: ck ::]

lazy - how many months have u been doin integration for

uve made like a million threads on integration!

 

[Crikket]

maybe it's his favourite bit in 4 unit maths?
my maths teacher makes us do random integration questions in the middle of a conics lesson just so we don't forget it

 

[ToO LaZy ^*]

Originally posted by J0n
The thing is, the standard integral is for int (1 / sqrt(a² - x²) ) - with no coefficient in front of x (just 1) .'. you have to make your integral like that (let u = 2x)

ohhhhhhhhhhhhh...i get it..

Originally posted by :: ryan.cck ::
lazy - how many months have u been doin integration for

uve made like a million threads on integration!

hahah..lol, yeah i know.
we're a slow class..well only coz we have 2 periods/week = 2 hours

but now we've started conics..