a. integral (3-2/x²+6/x³)dx b. F'(x) = x-2/x² ; F(-4)=7

Penyelesaian:

a. ∫ [tex]3 - \frac{2}{x^2} + \frac{6}{x^3} [/tex] dx
= ∫ 3 - 2x^-2 + 6x^-3 dx
= 3x + 2x^-1 - 3x^-2 + c
= [tex]3x + \frac{2}{x} - \frac{3}{x^2} + c[/tex]

b. ∫ [tex]x - \frac{2}{x^2} [/tex]
= ∫ x - 2x^-2 dx
= 1/2 x^2 + 2x^-1 + c
= [tex] \frac{1}{2}x^2 + \frac{2}{x} + c [/tex]

f(-4) = 7
f(-4) = [tex] \frac{1}{2}(-4)^2 + \frac{2}{-4} + c [/tex] = 7
= 8 - 1/2 + c = 7
c = -1/2

f(x) = [tex] \frac{1}{2}x^2 + \frac{2}{x} - \frac{1}{2} [/tex]