How do you determine the area of a region above the x-axis and below #f(x)=3+2x-x^2#?
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To determine the area of a region above the x-axis and below the curve (f(x) = 3 + 2x - x^2), you integrate the function over the interval where it intersects the x-axis. This involves finding the x-values where the function intersects the x-axis, 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 x-axis and below the curve represented by ( f(x) = 3 + 2x - x^2 ), you can use integration.
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First, find the x-values where the function intersects the x-axis by setting ( f(x) = 0 ) and solving for ( x ).
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Determine the bounds of integration based on the x-values obtained in step 1.
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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 x-axis 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 x-axis and below the curve.
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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.
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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