Question

Question about a primitive of a function.

I have a function f(x) = (-2x^2 + 4x)e^x.
determine the values of b and c such that
F(x) = (-2x^2 +bx + c)e^x is a primitive of f(x).

thanks a lot in advance

Answer 1

Find the antiderivative of f(x)

Answer 2

I would do that and get an answer with some constant +c i think

Answer 3

exactly

Answer 4

Is that the same c as in the question though?

Answer 5

How is the anti-derivative calculated then?

Answer 6

Or how is it technically different from integral?

Answer 7

I actually got it, thanks. I thought my calculator couldn't really do it without limits. But if i was to do this by hand, how would i find the anti-derivative?

Answer 8

\[\int f(x)\space dx = F(b) - F(a)\]
\[\int x^a \space dx = \frac{x^{a + 1}}{a + 1}\]

Answer 9

Actually, I take that back. I was thinking about definite integrals when I said that. When computing definite integrals, you usually don't deal with a plus c when calculating something like


\[\int^{2}_{4} x^4 dx = \frac{x^5}{5} \vert^2_4 = \frac{4^5}{5} - \frac{2^5}{5}\]

Answer 10

Right, I understand that a function like 2x can have an infinite number of its primitive functions like x^2 or x^2+6 etc. just generally called x^2 + c

if I integrate this function by whatever hard method there is (reverse chain rule) then will I not get a general +c still?

Answer 11

The plus c will definitely apply to indefinite integral

Answer 12

So my question would be this - are there in theory more than 1 answer for this question (for values of b and c) or is there just one correct answer?

Answer 13

answer given is (-2x^2 +8x -8) e^x

so b was found to be 8 and c -8

Answer 14

Originally, I suggested to find the anti-derivative, but I was mistaken because if you did that, you would end up with an \(x^3\) term for the leading term so my approach is way off here. Sorry for misleading you. Maybe someone else can help

Answer 15

:'[ this is hard..