# Integral Curves Equations

• Feb 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
• Feb 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.
• Feb 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
• Feb 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.
• Feb 14th 2010, 12:52 AM
Awsom Guy
Do I sub in the x values aswell.
• Feb 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
• Feb 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:
-12=C+D and
-13=C+D
How does this help.
Thanks
• Feb 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:
-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.
• Feb 14th 2010, 01:23 AM
Awsom Guy
What is the second equation then?
• Feb 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
• Feb 14th 2010, 01:27 AM
Awsom Guy
I got:
y=2x^2 + C + D.
• Feb 14th 2010, 01:31 AM
Jhevon
Quote:

Originally Posted by Awsom Guy
I got:
y=2x^2 + C + D.

it should be $2x^2 + Cx + D$
• Feb 14th 2010, 01:32 AM
Awsom Guy
How does that help though
• Feb 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
• Feb 14th 2010, 01:45 AM
Awsom Guy
yes I got it thanks.