4) Calcule a seguinte integral definida:.... Pergunta de ideia deLucasJairo

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4) Calcule a seguinte integral definida:

$\int\limits^2_0 {(2x-3)(4x^2+1)} \, dx$

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gabrieldoile Temos o seguinte:

$\int\limits^2_0 {(2x-3)(4x^2 + 1)} \, dx$

Assim:

$\int {(2x-3)(4x^2 + 1)} \, dx = \int {8x^3 + 2x - 12x^2 - 3} \, dx \\ \\ 
 \int {8x^3 + 2x - 12x^2 - 3} \, dx = \int {8x^3} \, dx + \int {2x} \, dx - \int {12x^2} \, dx - \int {3} \, dx \\ \\ 
8\int {x^3} \, dx + 2\int {x} \, dx - 12\int {x^2} \, dx - \int {3} \, dx \\ \\ 
8 \cdot \frac{x^4}{4} + 2 \cdot \frac{x^2}{2} - 12 \cdot \frac{x^3}{3} - 3x \\ \\ 
2x^4 + x^2 - 4x^3 - 3x$

Logo:

$\int\limits^2_0 {2x^4 + x^2 - 4x^3 - 3x} \, dx \\ \\ 
(2 \cdot 2^4 + 2^2 - 4 \cdot 2^3 - 3 \cdot 2) - (2 \cdot 0^4 + 0^2 - 4 \cdot 0^3 - 3 \cdot 0) \\ \\ 
= (32 + 4 - 4 \cdot 8 - 6) - 0 \\ \\ 
= 32 + 4 - 32 - 6 \\ \\ 
= -2$

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