How do you get the antiderivative for C'(x) = 20-(x/200) to be complete when I only know that I'm using Right Riemann sum with n=5 after. I know the antiderivative would be C=20x-(1/400)x^2+K (K substituting for what normally would be C since that is already used) but how do I get K so I can actually use the function?

Question

How do you get the antiderivative for C'(x) = 20-(x/200) to be complete when I only know that I'm using Right Riemann sum with n=5 after.  I know the antiderivative would be C=20x-(1/400)x^2+K (K substituting for what normally would be C since that is already used) but how do I get K so I can actually use the function?

oobleck · Accepted Answer

not sure what you're after here. If you want the area on the interval [0,5] then K does not matter. A definite integral C(5)-C(0) will subtract off the K. Only indefinite integrals have the unknown constant.

If you need to pin down K, then you have to know the value of C for some x. For example, if C(0) = 10, then
C=20x-(1/400)x^2+10

oobleck · Answer

my bad, as I noted on your previous post. The Riemann sum gives the area under the curve for C'(x). That area approximates the function C(x). So use values of C' for x=1,2,3,4,5.