Hasil dari ∫(2x^3-9x^2+4x-5)dx

Hasil dari $\int (2 x^{3} - 9 x^{2} + 4 x - 5) d x = \dots$

A. $\frac{1}{2} x^{4} - 6 x^{3} + 2 x^{2} - 5 x + C$

B. $\frac{1}{2} x^{4} - 6 x^{3} + x^{2} - 5 x + C$

C. $\frac{1}{2} x^{4} - 3 x^{3} + x^{2} - 5 x + C$

D. $\frac{1}{2} x^{4} - 3 x^{3} + 2 x^{2} - 5 x + C$

E. $\frac{1}{2} x^{4} - 6 x^{3} - 2 x^{2} - 5 x + C$

Penyelesaian

Diketahui:

$\int (2 x^{3} - 9 x^{2} + 4 x - 5) d x$

Jawab

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

$\int (2 x^{3} - 9 x^{2} + 4 x - 5) d x$

$= \frac{2}{3 + 1} x^{3 + 1} - \frac{9}{2 + 1} x^{2 + 1} + \frac{4}{1 + 1} x^{1 + 1} - 5 x + C$

$= \frac{2}{4} x^{4} - \frac{9}{3} x^{3} + \frac{4}{2} x^{2} - 5 x + C$

$= \frac{1}{2} x^{4} - 3 x^{3} + 2 x^{2} - 5 x + C$

Jawaban: D

Muda Berkarya Intelektual Normatif

MBIN