Question

integration

Answer 1

\[f(x) = (\int\limits_{0}^{1}f(x)dx )x^{2} + (\int\limits_{0}^{2} f(x) dx )x + (\int\limits_{0}^{3} f(x) dx ) + 1 \]
how to find the value of f(4)

Answer 2

in terms of \(F(x)\) [ where \(\tfrac{\mathrm dF(x)}{\mathrm dx}=f(x)\) ] ?

Answer 3

option

Answer 4

woah.... it's hard!!

Answer 5

@zepdrix @wio @ParthKohli @Kainui

Answer 6

Trying to make it easier to read while i think about what to do\[\large f(x) = x^2\int\limits\limits\limits_{0}^{1}f(x)dx +x\int\limits\limits\limits_{0}^{2} f(x) dx + \int\limits\limits\limits_{0}^{3} f(x) dx + 1\]

Answer 7

well, the options are :
A. -3 D. 0
B. -2 E. 1
C. -1

what the start to do this poblem guys ?

Answer 8

\[
F'(x) = f(x)
\]\[
F'(x) = x^2(F(1)-F(0)) +x(F(2)-F(0))+ (F(4)-F(0))+1
\]

Answer 9

Are you saing that \(f(x)\) is a constant...?

Answer 10

Can you post a screenshot of this problem? Something seems to be missing.

Answer 11

i m not sure f(x) is a constant or not, @wio
i got this question from this site :
http://mathsolar.com/thread/post/53ab71863a4c1

Answer 12

Integrate from 0 to t and: \[
F(t) - F(0) = \frac13 t^3(F(1)-F(0)) + \frac 12t^2(F(2)-F(0)) + t(F(3)-F(0) + 1)
\]

Answer 13

the site has a worked out solution underneath

Answer 14

i m still confusing with behind int f(x), there is x, x^2. if i integrate f(x) what happened with x, and x^2 ?

Answer 15

The definite integrals are all constants.
So f(x) = Ax^2 + Bx + C + 1
Compare this to the given f(x). You can find A, B and C. Substitute in f(x) and then find f(4).