# Thread: Working out +C from integration

1. ## Working out +C from integration

Hey I was doing an integration question and I got the answer:

${y}=6{x}-2{x}^2-{x}^3+c$ the final marking point on the question was to work out c. The point went through the origin so the end answer (which I had to look up) was ${y}=6{x}-2{x}^2-{x}^3$. How do I work out c if say the curve ${y}=6{x}-2{x}^2-{x}^3+c$ went through $(3,2)$?

2. Originally Posted by Envy
Hey I was doing an integration question and I got the answer:

${y}=6{x}-2{x}^2-{x}^3+c$ the final marking point on the question was to work out c. The point went through the origin so the end answer (which I had to look up) was ${y}=6{x}-2{x}^2-{x}^3$. How do I work out c if say the curve ${y}=6{x}-2{x}^2-{x}^3+c$ went through $(3,2)$?
Sub in x=3 and y=2 and solve for c.

So ${y}=6{x}-2{x}^2-{x}^3+c$ went through $(3,2)$

becomes ${2}=6(3)-2(3)^2-(3)^3+c \:, \: c = 2+27+18-18= 29$

3. ## rearrange?

so literally rearrange to make c the subject and substitute in the x and y values?

4. Originally Posted by Envy
so literally rearrange to make ${c}$ the subject and substitute the ${x}$ and ${y}$?
Yeah, that's all there is to it.

5. ## Thanks

Cheers, it seems so obvious now

6. Originally Posted by Envy
Cheers, it seems so obvious now
Yeah, it's even simpler when it's the origin because it usually means that c=0. It only really gets harder to decide when you get an initial condition