Integral Function
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topsquark
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Okay, I've got a bug in my calculations but this should work. I'll give you the general lay-out and let you fill in the rest. If you have questions just let us know.
First f(x) has to be a quadratic. The integrals are just constants so you will have \(\displaystyle a = \int_{-1}^0 f(x) ~ dx\) and similar for b and c. Thus \(\displaystyle f(x) = ax^2 + bx + c + 1\). Calculate these integrals out in terms of a, b, and c.
You will now have three equations in a, b, c. Solve the system and there you go.
-Dan
First f(x) has to be a quadratic. The integrals are just constants so you will have \(\displaystyle a = \int_{-1}^0 f(x) ~ dx\) and similar for b and c. Thus \(\displaystyle f(x) = ax^2 + bx + c + 1\). Calculate these integrals out in terms of a, b, and c.
You will now have three equations in a, b, c. Solve the system and there you go.
-Dan
NovErdy
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topsquark
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\(\displaystyle a = \int_{-1}^0 f(x) ~ dx\)
\(\displaystyle b = \int_{-2}^0 f(x) ~ dx\)
\(\displaystyle c = \int_{-3}^0 f(x) ~ dx\)
And we have that \(\displaystyle f(x) = a x^2 + bx + (c + 1)\)
Plugging this into the first equation gives
\(\displaystyle a = \int_{-1}^0 (ax^2 + bx + (c + 1))~dx\)
Do the integral and you have an equation for a in terms of a, b, and c. Do all three integrals and you will have a set of 3 equations in 3 unknowns. Solve this for a, b, and c.
Give it a try and let us know if you get stuck.
-Dan
Harry_the_cat
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Yes of course. It's just a normal equation in 3 variables.