# How do you find the area between the curves #y=x^2-4x+3# and #y= 3+4x-x^2#?

Hello !

Answer is

First, graph the curves. You get

Second, calculate the abscises of intersection : solve

so

then

Finally, calculate the area

Then

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To find the area between the curves y = x^2 - 4x + 3 and y = 3 + 4x - x^2, first, determine the points of intersection by setting the two equations equal to each other and solving for x. Then integrate the absolute difference between the two curves over the interval of intersection.

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To find the area between the curves (y = x^2 - 4x + 3) and (y = 3 + 4x - x^2), you first need to determine the points of intersection between the two curves by setting them equal to each other and solving for (x). Then, integrate the absolute difference between the two functions with respect to (x) over the interval of intersection. The area can be calculated using the formula:

[ \text{Area} = \int_{a}^{b} |f(x) - g(x)| , dx ]

where (f(x)) and (g(x)) are the two functions, and (a) and (b) are the x-coordinates of the points of intersection.

Once you've found the points of intersection, integrate the absolute difference between the two functions over the interval between these points. The result will give you the area between the curves.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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