easy integral (1 Viewer)

[blackbunny]

integral of 1/(sqrt(4-x^2)) is sin^-1 (2x)....?

 

[richz]

dunno cbb looking at the standard integral sheet...

edit: mite as well its sin^-1 (x/2) +c

 

[blackbunny]

i was close

 

[blackbunny]

why is it x/2 this is what i dont get

 

[KFunk]

integral of 1/(sqrt(4-x^2))

let x = 2sinθ ---> dx = 2cosθdθ

∫ dx/√(4-x²)
= ∫ 2cosθ/√(4[1-sin²θ]) dθ
= ∫ 2cosθ/√[4cos²θ] dθ
= ∫ 1 dθ
= θ

since x = 2sinθ
x/2 = sinθ
θ = sin^-1(x/2)

therefore ∫ dx/√(4-x²) = sin^-1(x/2)

 

[richz]

why is it x/2 this is what i dont get

use the standard integrals sheet....

 

[thunderdax]

Haven't you done inverse trig functions yet? Because this is almost the easiest question you can get.

 

[rama_v]

See the standard integral is 1/sqrt[a^2-x^2] = sin^-1 (x/a)
In this instance:
1/sqrt[4-x^2] , a= 2 so therefore the integral is sin^-1(x/2)

 

[SaHbEeWaH]

and, isn't it abit late to be doing these questions
like 1 year

 

[rama_v]

and, isn't it abit late to be doing these questions
like 1 year

Not really, we only did inverse trig a few weeks ago...Different schools do teh topics in different order, and a lot of it depends on what u do in 2 unit...

 

[Pace_T]

i think he's referring to the thread starter's hsc finish date - 2004
hehe

EDIT: the loading up page showed ur reply after mine lol!!

 

[SaHbEeWaH]

i was referring to this:

blackbunny
Senior Member



HSC: <b>2004</b>

 

[rama_v]

ahh ok sorry about that lol