Mathematics, 08.11.2019 00:31 lexhorton2002
Find the area of the shaded region f(x)= x^3+x^2-6x and g(x)=6x. the bounds are [-4,0].
Answers: 3
![\bf \begin{cases} f(x)=x^3+x^2-6x\\\\ g(x)=6x \end{cases}\qquad \displaystyle \int\limits_{-4}^{0}\ \begin{array}{llll} [ceiling]&-&[floor]\\ f(x)&&g(x) \end{array} \\\\\\ thus \\\\\\ \displaystyle \int\limits_{-4}^{0}\ [[x^3+x^2-6x]-[6x]]dx\implies \displaystyle \int\limits_{-4}^{0}\ x^3+x^2-12x \\\\\\ \left. \cfrac{x^4}{4}+\cfrac{x^3}{3}-6x^2 \right]_{0}^{-4}](/tpl/images/0364/6241/ddf9b.png)
![Find the area of the shaded region f(x)= x^3+x^2-6x and g(x)=6x. the bounds are [-4,0].](/tpl/images/0364/6241/b039e.jpg)
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Find the area of the shaded region f(x)= x^3+x^2-6x and g(x)=6x. the bounds are [-4,0]....
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