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# Integration help? watch

1. 3).

A curve passes through (0,1) and satisfies the differential equation dy/dx= (4-y^2)^1/2. Find its equation and sketch its graph.

Basically I have no idea how to integrate it?

Any hints would be appreciated.
2. (Original post by Super199)
3).

A curve passes through (0,1) and satisfies the differential equation dy/dx= (4-y^2)^1/2. Find its equation and sketch its graph.

Basically I have no idea how to integrate it?

Any hints would be appreciated.
use the substitution y = 2sinθ
3. (Original post by Super199)
3).

A curve passes through (0,1) and satisfies the differential equation dy/dx= (4-y^2)^1/2. Find its equation and sketch its graph.

Basically I have no idea how to integrate it?

Any hints would be appreciated.
Use a substitution, or if you prefer. or look it up in a table - it's a standard result.
4. (Original post by TeeEm)
use the substitution y = 2sinθ
(Original post by joostan)
Use a substitution, or if you prefer. or look it up in a table - it's a standard result.
I think I am missing something here. What is the standard result I am supposed to see? I am not sure if were taught this, or it may be some c3/c4 stuff I have forgotten.
5. (Original post by Super199)
I think I am missing something here. What is the standard result I am supposed to see? I am not sure if were taught this, or it may be some c3/c4 stuff I have forgotten.
The integral:

for a given constant is a standard result.
6. (Original post by joostan)
The integral:

for a given constant is a standard result.
oh right yeah that gives inverse sine right. sin^-1(x/a)+c
7. (Original post by Super199)
I think I am missing something here. What is the standard result I am supposed to see? I am not sure if were taught this, or it may be some c3/c4 stuff I have forgotten.
It is only standard for further mathematicians,,, Just use the substitution
8. (Original post by TeeEm)
It is only standard for further mathematicians,,, Just use the substitution
It seems like a lot more effort. How does knowing the standard result help?
9. (Original post by Super199)
It seems like a lot more effort.
I am sorry to hear that.

(Original post by Super199)
How does knowing the standard result help?
you can have the answer in 3 lines
(assuming you have gone the long hard substitution way a few times to have an appreciation of the techniques involved)
10. (Original post by TeeEm)
I am sorry to hear that.

you can have the answer in 3 lines
(assuming you have gone the long hard substitution way a few times to have an appreciation of the techniques involved)
Decent, care to inform me on how that is done.

Like I probably could have done it if it was 1/(4-y^2). As that is sin^-1(y/2) +c . But yeah we have one over that so how does the integral change?
11. (Original post by Super199)
Decent, care to inform me on how that is done.

Like I probably could have done it if it was 1/(4-y^2). As that is sin^-1(y/2) +c . But yeah we have one over that so how does the integral change?
I am not following

once you separate variables you do have 1/over
12. (Original post by TeeEm)
I am not following

once you separate variables you do have 1/over
ah I got it now cheers bae
13. (Original post by Super199)
ah I got it now cheers bae
all the best

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