Question

Resolva a integral definida:

$\int\limits^2_0$(3x² + 2x)² dx

Answer 1

Olá Caahta 

(3x² + 2x)² = 9x⁴  + 12x³  + 4x² 


F(x) = ∫ (9x⁴  + 12x³  + 4x²) dx = 9x⁵/5 + 3x⁴ + 4x³/3

F(2) = 9*32/5 + 3*16 + 4*8/3 

F(2) = 27*32/15 + 15*3*16/15 + 20*8/15 = 1774/15 

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Answer 2

$\int\limits^2_0 {(3x^2+2x)^2} \, dx \\ \\ \int\limits^2_0 {(3x^2)^2+2.3x^2.2x+(2x)^2} \, dx \\ \\ \int\limits^2_0 {(9x^4+12x^3+4x^2)} \, dx \\ \\ 9\int\limits^2_0 {x^4} \, dx +12\int\limits^2_0 {x^3} \, dx +4\int\limits^2_0 {x^2} \, dx \\ \\ 9.( \frac{x^{4+1}}{4+1})|^2_0+12.( \frac{x^{3+1}}{3+1}) |^2_0+4.( \frac{x^{2+1}}{2+1} ) |^2_0 \\ \\ 9.( \frac{x^{5}}{5})|^2_0+12.( \frac{x^{4}}{4}) |^2_0+4.( \frac{x^{3}}{3} ) |^2_0$

$9.( \frac{2^{5}-0^5}{5})+12.( \frac{2^{4}-0^4}{4}) +4.( \frac{2^{3}-0^3}{3} ) \\ \\ 9.( \frac{32}{5})+12.( \frac{16}{4}) +4.( \frac{8}{3} ) \\ \\ \frac{288}{5}+48+ \frac{32}{3} \\ \\ \frac{3*288+15*48+5*32}{15} \\ \\ \boxed{\frac{1744}{15}} \approx 116,27$