Tentukan \( \displaystyle \int_0^2 x(3x+5) \ dx \).
- 18
- 16
- 15
- 10
- 6
Pembahasan:
Ingat bahwa \( \int ax^n dx = \frac{a}{n+1}x^{n+1}+C \) sehingga:
\begin{aligned} \int_0^2 x(3x+5) \ dx &= \int_0^2 (3x^2+5x) \ dx \\[8pt] &= \left[ \frac{3}{3}x^3+\frac{5}{2}x^2 \right]_0^2 \\[8pt] &= \left[ x^3+\frac{5}{2}x^2 \right]_0^2 \\[8pt] &= \left[2^3+\frac{5}{2}(2)^2\right]-\left[ 0^3+\frac{5}{2}(0)^2 \right] \\[8pt] &= 18-0 = 18 \end{aligned}
Jawaban A.