# How do you find the area of the region between the graphs of #y=x^2# and #y=-x# from x=0 to x=3?

Given two functions, f(x) and g(x), where f(x) > g(x) in a region [a,b] the area between the two functions is:

In the region [0,3], f(x) = x^2 and g(x) =-x.

Therefore the area of the between the two function in this region is:

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To find the area of the region between the graphs of (y = x^2) and (y = -x) from (x = 0) to (x = 3), you need to integrate the absolute difference between the two functions over the given interval.

The absolute difference between the functions (y = x^2) and (y = -x) is (|x^2 - (-x)| = |x^2 + x|).

To find the area, integrate (|x^2 + x|) with respect to (x) from (x = 0) to (x = 3).

After integration, the result will give you the area of the region between the graphs of the two functions over the specified interval.

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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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