How do you find the area bounded by #y=4-x^2#, the x and y axis, and x=1?
First picture what this region would look like by envisioning its graph (or just looking straight at it):
graph{4-x^2 [-9.54, 10.46, -3.92, 6.08]}
graph{(4-x^2)sqrt(x-x^2)/sqrt(x-x^2) [-2, 3, -1, 4.72]}
Integrating (finding the antiderivative) and keeping the bounds gives:
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To find the area bounded by the curve y = 4 - x^2, the x and y axes, and the line x = 1, we integrate the function from the x-axis up to the curve and then subtract the area under the x-axis (which is negative).
The integral setup is: ∫[0 to 1] (4 - x^2) dx.
Evaluating this integral gives the area bounded by the curve, the x-axis, and the line x = 1.
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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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