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

Consider the function:

The area bounded by the curves is then:

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Use the integral of the difference between the two functions:

Here is a graph of

and

Pleases observe that equation [2] is greater than equation [1] in the enclosed region; this means that the integral is of the form:

Simplify the integrand:

We need to find the values of "a" and "b" by finding the two x coordinates where the two parabolas intersect. We can do this by setting the integrand equal to 0 and then solving for the two values of x:

Multiply by -1:

This factors into:

The above are the values of "a" and "b":

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To find the area bounded by the curves (y = x^2 + 2x - 4) and (y = -2x^2 + 4x - 3), you need to first find the points of intersection between the two curves. These points will represent the limits of integration.

Set the two equations equal to each other and solve for (x) to find the points of intersection. Once you have the intersection points, you can integrate the absolute difference between the two curves from the leftmost intersection point to the rightmost intersection point to find the area bounded by 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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