# Write a definite integral that yields the area of the region. (Do not evaluate the integral.)?

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To write a definite integral that yields the area of a region, you need to specify the limits of integration and the function that represents the region's boundary. The definite integral will then integrate this function over the specified interval to calculate the area enclosed by the region.

For example, if you have a region bounded by the x-axis and the curve ( y = f(x) ) between the x-values ( a ) and ( b ), the definite integral representing the area of this region would be:

[ \int_{a}^{b} f(x) , dx ]

Similarly, if the region is bounded by two curves, say ( y = g(x) ) and ( y = h(x) ), between the x-values ( a ) and ( b ), the definite integral representing the area of this region would be:

[ \int_{a}^{b} [g(x) - h(x)] , dx ]

In both cases, the integral calculates the area under the curve(s) between the specified x-values.

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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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