Integral Curves Equations

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February 14th 2010, 12:41 AM
Awsom Guy

Integral Curves Equations

Question:
For a curve y=h(x), the second derivative h''(x)=4, find the equation of the curve given that when x=1, y=-10 and when x=2, y=-9.

I know that y'= 4x + C
But I don't what to do next and how to place these points to find the equation.
Any help io good.
Thanks
February 14th 2010, 12:44 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

Question:
For a curve y=h(x), the second derivative h''(x)=4, find the equation of the curve given that when x=1, y=-10 and when x=2, y=-9.

I know that y'= 4x + C
But I don't what to do next and how to place these points to find the equation.
Any help io good.
Thanks

find y.

then, use the given points to set up two simultaneous equations to find the arbitrary constants of integration.
February 14th 2010, 12:47 AM
Awsom Guy

Don't I already have y, I can't integrate this equation as I don't know enough to get to y, I know how to get to y'.
Thanks
February 14th 2010, 12:50 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

Don't I already have y, I can't integrate this equation as I don't know enough to get to y, I know how to get to y'.
Thanks

no, you found y', you need to integrate that to get to y. you will get another arbitrary constant, call it D. then solve for C and D using the points you were given.
February 14th 2010, 12:52 AM
Awsom Guy

Do I sub in the x values aswell.
February 14th 2010, 12:56 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

Do I sub in the x values aswell.

when you have y, you sub in corresponding x and y values at the same time. your last two equations must only have C and D as unknowns. that's how you'll manage to solve for them
February 14th 2010, 12:58 AM
Awsom Guy

but I will have town unknown values C and D how am I meant to figure out the two values:
The answers:
-12=C+D and
-13=C+D
How does this help.
Thanks
February 14th 2010, 01:07 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

but I will have town unknown values C and D how am I meant to figure out the two values:
The answers:
-12=C+D and
-13=C+D
How does this help.
Thanks

your second equation is not right. and you've solved simultaneous equations before, yeah? That's definitely something you'd have to have done before calculus.
February 14th 2010, 01:23 AM
Awsom Guy

What is the second equation then?
February 14th 2010, 01:25 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

What is the second equation then?

tell me what expression you got for y
February 14th 2010, 01:27 AM
Awsom Guy

I got:
y=2x^2 + C + D.
February 14th 2010, 01:31 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

I got:
y=2x^2 + C + D.

it should be $2x^2 + Cx + D$
February 14th 2010, 01:32 AM
Awsom Guy

How does that help though
February 14th 2010, 01:41 AM
Jhevon

Quote:

Originally Posted by Awsom Guy

How does that help though

fix your second equation now and see.

you can subtract one from the other to start finding your unknowns
February 14th 2010, 01:45 AM
Awsom Guy

yes I got it thanks.