Hasil dari ∫(x-3)(x+2) dx

Hasil dari $\int (x - 3) (x + 2) d x = \dots$

A. $\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 6 x + C$

B. $\frac{1}{3} x^{3} - \frac{5}{2} x^{2} - 6 x + C$

C. $\frac{1}{3} x^{3} - \frac{3}{2} x^{2} - 6 x + C$

D. $\frac{1}{3} x^{3} + \frac{3}{2} x^{2} - 6 x + C$

E. $\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x + C$

Penyelesaian

Diketahui:

$\int (x - 3) (x + 2) d x$

Jawab

RUMUS: $f (x) = a x^{n} \to \int f (x) d x = \frac{a}{n + 1} x^{n + 1}$

$\int (x - 3) (x + 2) d x = \int (x^{2} - x - 6) d x$

$= \frac{1}{2 + 1} x^{2 + 1} - \frac{1}{1 + 1} x^{1 + 1} - 6 x + C$

$= \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x + C$

Jawaban: E

Muda Berkarya Intelektual Normatif

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