Soal Matematika Kelas XII no 33

33. ഽ x√x dx sama dengan ...

a. 1/2 x√x + C

b. 2 1/2 x^2 √x + C

c. 2 1/2 x√x + C

d. 2/5 x √x + C

e. 2/3 x^2 √x + C

Jawaban :

ഽ x√x

= ഽ x . x^1/2

= ഽ x^3/2

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

= 1/(5/2) x^(5/2) + C

= 2/5 x^(5/2) + C

= 2/5 x^2 . x^1/2 + C

= 2/5 x^2 √x + C