Question

Calcule a integral da função f left parenthesis x right parenthesis equals space 2 x cubed plus x squared minus 5 x , no intervalo de (0 a 2)

Answer 1

A função é $f(x)=2x^3+x^2-5 x$

A integral será 

$I=\int_0^2{2x^3+x^2-5 x}\,dx \\ \\ I=\int2x^3+x^2-5x \, dx |_0^2\\ \\ I=\frac{x^4}{2}+\frac{x^3}{3}-\frac{5x^2}{2} |_0^2\\ \\ I=\frac{2^4}{2}+\frac{2^3}{3}-\frac{5\cdot 2^2}{2} -0\\ \\ I= 8+\frac{8}{3}-10\\ \\ I=\frac{8}{3}-2 \\ \\ I=\frac{2}{3}.$