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

First let define the definite integral we need:

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To find the area bounded by the curve ( y = 3 - 2x - x^2 ) and the x-axis, you would integrate the absolute value of the function between its roots with respect to x. This is because the given function may cross the x-axis, creating regions above and below the x-axis. The area can be computed by finding the absolute difference between the integrals of the function above and below the x-axis. Thus, the steps would be:

- Find the roots of the equation ( y = 3 - 2x - x^2 ) by setting ( y = 0 ) and solving for ( x ).
- Integrate the absolute value of the function between these roots with respect to ( x ).
- The result of the integration gives the area bounded by the curve and the x-axis.

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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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