Question

f(x)= x ao cubo - 2x ao quadrado - 5x. Qual a área limitada pela curva nos intervalos [-1,0]

Answer 1

$f(x)=x^3-2x^2-5x$

$A=\int\limits_{-1}^{0}(x^{3}-2x^{2}-5x)~dx$

$A=\frac{x^{4}}{4}-\frac{2x^{3}}{3}-\frac{5x^2}{2}|_{-1}^{0}$

$A=-\left(\frac{(-1)^4}{4}-\frac{2*(-1)^3}{3}-\frac{5*(-1)^2}{2}\right)$

$A=-<span>\frac{1}{4}-\frac{2}{3}+\frac{5}{2}$

$A=-<span>\frac{3}{12}-\frac{8}{12}+\frac{30}{12}$

$\boxed{\boxed{A=-\frac{19}{12}}}$