Question

O resultado da integral definida ∫2^3 (3x2+ 2x+2) dx é:

Alternativa 1: 16
Alternativa 2: 26
Alternativa 3: 6
Alternativa 4: - 6
Alternativa 5: -11

Answer 1

$\int\limits^3_2 ({3x^2 + 2x + 2}) \, dx = \frac{3.x^3}{3} + \frac{2.x^2}{2} + 2x$

$\int\limits^3_2 ({3x^2 + 2x + 2}) \, dx = x^3 + x^2 + 2x$

Então :

$\int\limits^3_2 ({3x^2 + 2x + 2}) \, dx = \int\limits^3_0 ({3x^2 + 2x + 2}) \, dx - \int\limits^2_0 ({3x^2 + 2x + 2}) \, dx$

$\int\limits^3_2 ({3x^2 + 2x + 2}) \, dx = (3)^3 + (3)^2 + 2.3 - (2)^3 - (2)^2 - 2.2$


$\int\limits^3_2 ({3x^2 + 2x + 2}) \, dx = 27 + 9 + 6 - 8 - 4 - 4 = 26$