Question

Integral persamaan kurva;
Tentukan f(x) jika diketahui sebagai berikut.
f'(x)= ax+b ; f(1)=0 ; dan f(-1)=4 ; dan f(3)=8

Answer 1

f'(x) = ax+b
f(x) = (1/2)ax^2 + bx + c

f(1) = 0
f(-1) = 4
f(3) = 8

f(1) = (1/2)a(1)^2 + b(1) + c
0 = (a/2) + b + c.......(1)

f(-1) = (1/2)a(-1)^2 + b(-1) + c
4 = (a/2) - b + c.........(2)

f(3) = (1/2)a(3)^2 + b(3) + c
8 = (9a/2) + 3b + c......(3)

(1) 0 = (a/2) + b + c
(2) 4 = (a/2) - b + c
_________________ -
-4 = 2b
-2 = b.........(4)

(3) 8 = (9a/2) + 3b + c
(2) 4 = (a/2)  -  b + c
___________________ -
4 = 4a + 4b
1 = a + b
1 = a + (-2)
3 = a.........(5)

0 = (a/2) + b + c
0 = (3/2) + (-2) + c
(1/2) = c........(6)

f(x) = (1/2)ax^2 + bx + c
f(x) = (1/2).3.x^2 + (-2)x + (1/2)
f(x) = (3/2)x^2 - 2x + (1/2)