Soal Matematika Kelas XII no 37

37. ഽ(1/(2x√x)) = ...

a. - 1/√x + C

b. - 1/x√x + C

c. 1/√x + C

d. - 2/√x + C

e. - 1/2√x + C

Jawaban :

ഽ(1/(2x√x))

= ഽ(1/(2x^(3/2))

= ഽ(1/2 . 1/x^(3/2))

= ഽ(1/2 . x^ - (3/2))

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

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

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

= - x^(-1/2) + C

= - 1/x^1/2 + C

= - 1/√x + C

Jawaban : A