Year 12s: what will be the first way you research your future options? >>

integration any1?

need to use the substitution x=sin theta
to integrate 1/(1-x^2)^(3/2)

ive worked out dx = dtheta cos theta
and subbed values in but i cant seem to get the right answer which is x/(1-x^2)^(1/2)

ive got 1/cos^2 theta dtheta so far...

Reply 1

cj_134

and 1/cos^2 theta = sec^2 theta , when u integrate that u get tan theta, no?

Reply 2

Thisisj

Original post by cj_134

and 1/cos^2 theta = sec^2 theta , when u integrate that u get tan theta, no?[/QU
yh .. but thats not the answer .. :s-smilie:

Reply 3

cj_134

yes, then replace ur theta with your x, not directly, notice tan theta = sin theta / cos theta , sin theta = x and cos theta = (1-x^2)^1/2 , which gives the answer you want in terms of x, and dont forget your constant

Reply 4

Thisisj

Original post by cj_134

why is cos theta = (1-x^2)^1/2?

Reply 5

EEngWillow

Original post by Thisisj

why is cos theta = (1-x^2)^1/2?

sin^2(\theta) + cos^2(\theta) = 1

Reply 6

cj_134

Original post by Thisisj

why is cos theta = (1-x^2)^1/2?

ok, you know sin^2 theta + cos^2 theta = 1
so cos^2 theta = 1-sin^2 theta
cos theta = (1 - sin^2 theta) ^1/2
you know sin theta = x
hence cos theta = (1-x^2)^1/2

Reply 7

Thisisj

Original post by EEngWillow

sin^2(\theta) + cos^2(\theta) = 1

Original post by cj_134

ok, you know sin^2 theta + cos^2 theta = 1
so cos^2 theta = 1-sin^2 theta
cos theta = (1 - sin^2 theta) ^1/2
you know sin theta = x
hence cos theta = (1-x^2)^1/2

oooooo right...
thanks guys :smile:

Reply 8

Thisisj

Original post by cj_134

ok, you know sin^2 theta + cos^2 theta = 1
so cos^2 theta = 1-sin^2 theta
cos theta = (1 - sin^2 theta) ^1/2
you know sin theta = x
hence cos theta = (1-x^2)^1/2

do you know any good websites to help me or show a step by step method because im stuck on a few of these types of questions???