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Please, Sketch the area to make me understand, this question from area bounded curve of integral calculus. Necessary to solve.

John Wayland Bales
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user409382
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    Welcome to Stack Exchange. You should always state what you have already tried or how you think the problem might be approached or you risk getting down-votes. One graphing resource you can use is desmos.com. You can type the two equations into the interface and see what the graphs look like and where they intersect. – John Wayland Bales Feb 04 '17 at 01:58
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    Do you know how to graph the parabola? Do you know how to graph the line? If you do, graph them and then look at the region they form a border for. – Dave Feb 04 '17 at 02:01
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    Set the two equations equal to each other and solve the resulting quadratic equation to find the two points of intersection. – John Wayland Bales Feb 04 '17 at 02:03

1 Answers1

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From what I can tell, you want to find the area between the red and blue. The yellow line is just blue minus red or $-x^2+5x-6$. Integrating (don't know LaTeX well enough) gives that the area as

$F(3)-F(2)=\frac{1}{6}$ where $F(x) = -\frac{1}{3} x^3 + \frac{5}{2} x^2 - 6x +C$ is the antiderivative

EDIT: okay, I guess I need to show that $2,3$ are roots. But $-(x-2)(x-3)=-x^2+5x-6$

Wen
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