Please, Sketch the area to make me understand, this question from area bounded curve of integral calculus. Necessary to solve.
Find the area of the segment of the parabola $y=x^2-7x+9$ cut off by the line $y=3-2x$.
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definite-integrals
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2Welcome 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. – 2017-02-04
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1Do 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. – 2017-02-04
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1Set the two equations equal to each other and solve the resulting quadratic equation to find the two points of intersection. – 2017-02-04
1 Answers
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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 $-(x-2)(x-3)=-x^2+5x-6$
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1Thanks a lot.. I try that way., but i don't take the yellow curve – 2017-02-04