How do you determine the area of a region above the xaxis and below #f(x)=3+2xx^2#?
I would start trying to "see" this area:
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To determine the area of a region above the xaxis and below the curve (f(x) = 3 + 2x  x^2), you integrate the function over the interval where it intersects the xaxis. This involves finding the xvalues where the function intersects the xaxis, which are the roots of the equation (f(x) = 0). Once you have the interval, you integrate the absolute value of the function within that interval to find the area.
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To determine the area of a region above the xaxis and below the curve represented by ( f(x) = 3 + 2x  x^2 ), you can use integration.

First, find the xvalues where the function intersects the xaxis by setting ( f(x) = 0 ) and solving for ( x ).

Determine the bounds of integration based on the xvalues obtained in step 1.

Integrate the absolute value of the function from the lower bound to the upper bound. This ensures that the area is positive.
The integral ( \int_{a}^{b} f(x) , dx ) represents the area between the curve and the xaxis from ( x = a ) to ( x = b ).
Evaluate this integral using appropriate antiderivatives or integral techniques.
This will give you the area of the region above the xaxis and below the curve.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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