Soal Matematika Kelas XII no 39

39. ₁ഽ²(x - 1)/x^3 dx = ...

a. - 1 1/16

b. 1/8

c. 1

d. 1 1/2

e. 21/8

Jawaban : 

₁ഽ²(x - 1)/x^3 dx

= ₁ഽ²(x - 1) . x^-3 dx

= ₁ഽ²(x^-2 - x^-3) dx

= [1/(-2 + 1) x^(-2 + 1) - 1/(-3 + 1) x ^ (-3 + 1) ]₁²

= [ -x^-1 - 1/(-2) x ^ -2 ]₁²

= [ - 1/x + 1/2 . 1/x^2 ]₁²

= ( - 1/2 + 1/2 . 1/2^2) - (- 1/1 + 1/2 . 1/1^2)

= ( - 1/2 + 1/2 . 1/4) - (- 1 + 1/2 )

= (- 1/2 + 1/8) - (- 1/2)

= - 1/2  + 1/8 + 1/2

= 1/8

Jawaban : B