Diketahui \( \int_0^3 (x^2+px+2) \ dx = \frac{3}{2} \). Nilai \(p\) yang memenuhi adalah…
- \( -26 \)
- \( -13 \)
- \( -3 \)
- \( 3 \)
- \( 13 \)
(UN MTK IPA 2018)
Pembahasan:
\begin{aligned} \int_0^3 (x^2+px+2) \ dx &= \frac{3}{2} \\[8pt] \left[ \frac{1}{3}x^3+\frac{p}{2}x^2+2x \right]_0^3 &= \frac{3}{2} \\[8pt] \left( \frac{1}{3}(3)^3+\frac{p}{2}(3)^2+2(3) \right)-0 &= \frac{3}{2} \\[8pt] 9+\frac{9}{2}p+6 &= \frac{3}{2} \\[8pt] \frac{9}{2}p+15 &= \frac{3}{2} \\[8pt] 9p+30 &= 3 \\[8pt] 9p &= -27 \\[8pt] p &= -3 \end{aligned}
Jawaban C.