Soal Matematika Kelas XII no 36

 36. Jika f(x) = ഽ(1/3 x^2 - 2x + 5) dx dan f(0) = 5 , maka f(x) = ...

a. 1/9 x^3 + 5x + C

b. 2/3 x^3 - x^2 + 5x + 9

c. 2/3 x^3 - 2x + 5x + 5

d. 1/9 x^3 - x^2 + 5x + 5

e. 1/9 x^3 - 2x^2 + 5x + 3

Jawaban :

f(x) = ഽ(1/3 x^2 - 2x + 5)

f(x) = 1/3 . 1/(2 + 1) . x^(2+ 1) - 2 . 1/(1 + 1) . x^(1 + 1) + 5x + C

f(x) = 1/3 . 1.3 x^3 - 2 . 1/2 . x^2 + 5x + C

f(x) = 1/9 x^3 - x^2 + 5x + C

diketahui :

f(0) = 5

f(x) = 1/9 x^3 - x^2 + 5x + C

f(0) = 1/9 . 0 - 0 + 0 + C

5 = C

maka, 

f(x) = 1/9 x^3 - x^2 + 5x + C

f(x) = 1/9 x^3 - x^2 + 5x + 5

Jawaban : D