Given-f-x-3-16-0-1-f-x-dx-x-2-9-10-0-2-f-x-dx-x-2-0-3-f-x-dx-4-Find-f-x-

Question Number 32323 by Joel578 last updated on 23/Mar/18

Given

f (x) = \frac{3}{16} (\int_{0}^{1} f (x) d x) x^{2} - \frac{9}{10} (\int_{0}^{2} f (x) d x) x + 2 (\int_{0}^{3} f (x) d x) + 4

Find f (x)

Answered by ajfour last updated on 23/Mar/18

l e t f (x) = {A x}^{2} + B x + C

\Rightarrow {A x}^{2} + B x + C = \frac{3}{16} (\frac{A}{3} + \frac{B}{2} + C) x^{2}

- \frac{9}{10} (\frac{8 A}{3} + 2 B + 2 C) x

+ 2 (\frac{27 A}{3} + \frac{9 B}{2} + 3 C) + 4

f o r x = 0

C = 18 A + 9 B + 6 C + 4

\Rightarrow 18 A + 9 B + 5 C = - 4

f o r x = 1

A + B + C = (\frac{1}{16} - \frac{12}{5} + 18) A +

(\frac{3}{32} - \frac{9}{5} + 9) B + (\frac{3}{16} - \frac{9}{5} + 6) C + 4

\Rightarrow 160 (A + B + C) = \dots \dots

Facebook Tweet Pin