Question

integral of dy/sqrt(4-y^2)?

Answer 1

a trig sub will work just dandy here

Answer 2

you'll want to complete the square and what you're left with use trig sub

Answer 3

\[\int\limits \frac{ dy }{ \sqrt{4-y ^{2}}}\]

Answer 4

Recall
1-sin^2(x)=cos^2(x)
so
4-4sin^2(x)=4cos^2(x)
so 4-(2sin(x))^2=4cos^2(x))

Answer 5

so it should be obvious what you want to replace y with

Answer 6

i am not good with trig identities

Answer 7

that's fine
i wrote the identity you needed

Answer 8

when is 4-(2sin(x))^2 the same as 4-y^2
when y= what?

Answer 9

oh.. i see
y=2sinx

Answer 10

so that is your sub

Answer 11

ok thank you!

Answer 12

@inkyvoyd I'm interested in the partial fractions way

Answer 13

but how do you do it with the sqrt around the 4-y^2 part/

Answer 14

@freckles ... you don't. I am such an idiot.

Answer 15

oh

Answer 16

wait freckles what happens after i sub in 2sinx

Answer 17

what happens to sqrt

Answer 18

y=2sin(x)
dy=?

Answer 19

And inky I don't believe you are an idiot. :p

Answer 20

dy=2cosx

Answer 21

that's the problem @freckles ... that's how idiots get to the top of important positions :P

Answer 22

dy=2cos(x) dx

Answer 23

So replace dy with 2cos(x) dx
replace y with 2sin(x)

Answer 24

and use the identity tht 4-4sin^2(x)=4cos^2(x)