inverse trig function? (1 Viewer)

[furryfish]

i was just wondering, is there a 3unit way of solving this

integration sign [(4-x^2)^1/2] dx

hope u understand that...
newayz, we havent done integration in 4u yet, so was wondering if there was any other way to solve this using 3u methods.

thanx

 

[FinalFantasy]

i was just wondering, is there a 3unit way of solving this

integration sign [(4-x^2)^1/2] dx

hope u understand that...
newayz, we havent done integration in 4u yet, so was wondering if there was any other way to solve this using 3u methods.

thanx

let I=int. sqrt (4-x²) dx
let x=2sin@
dx\d@=2cos@
I=int. (sqrt(4-4sin²@))2cos@ d@
=int. 2cos@2cos@d@=4int. cos²@ d@
=4int. (1\2)(cos2@+1)d@=2(1\2 sin2@+@)
=sin2@+2@+C

sin@=x\2, @=sin^-1 x\2
so I=sin 2(sin^-1 x\2)+2(sin^-1 x\2) +C

 

[haboozin]

yes, theres only 1 3unit method...

that is if they give the the substitution...

seeing as though you dont have a sub and it cant b solved normally.... then it isnt a 3u Q..


but keep in mind, you may be asked this question in 3unit... find the area:

2
(integral) sqrt(4-x^2) dx
-2



and to find that you must recognize that it is a semil circle and the area of a semi circle radius 2 = 2Pi units^2

the volume is also easy you can use ur sphere equation, which i dont know or integrate 4-x^2 which should be no problems.