integral 0 sampai 2 (x^2+4x+4) dx=...

Materi : Kalkulus
Bahasan : Integral Aljabar
Jawaban : 56/3

Langkah - langkah :
[tex] \int\limits^2_0 {(x^2 + 4x + 4)} \, dx \\ \\ = \frac{x^{2 + 1}}{2 + 1} + \frac{4x^{1 + 1}}{1 + 1} + \frac{4x^{0 + 1}}{0+1} \\ \\ = \frac{x^3}{3} + 2x^{2} + 4x \\ \\ = \frac{1}{3}x^3 + 2x^{2} + 4x \\ \\ Substitusi(2) \\ \\ = \frac{1}{3}(2)^3 + 2(2)^{2} + 4(2) \\ \\ = \frac{8}{3} + 16 = \frac{56}{3} \\ \\ Substitusi(0) \\ \\ = \frac{1}{3}(0)^3 + 2(0)^{2} + 4(0) \\ \\ = 0 \\ \\ = \frac{56}{3} - 0 \\ \\ = \frac{56}{3} [/tex]