Determine the area limited by curves:
$$f(x)=2x^3-3x^2+9x \\ g(x)=x^3-2x^2-3x$$
The correctly answer is: 25, How can I find it?
Determine the area limited by curves:
$$f(x)=2x^3-3x^2+9x \\ g(x)=x^3-2x^2-3x$$
The correctly answer is: 25, How can I find it?
Assuming that the limits of the interval are given $a
So, we can find the anti-derivatives for $f(x)$ and $g(x)$ and evaluate the difference at $a$, $b$. If we let $S$ to be the area below $f(x)$ and above $g(x)$ we need to calculate the area below $f(x)$ and above the $X$ axis minus the area below $g(x)$ above the $X$ axis: $$S = F(x)-G(x)|_{x=a}^{x=b}$$
Do you know what's the anti-derivative of a Polynomial?