How do you find the volume of the solid with base region bounded by the curve #y=1-x^2# and the #x#-axis if cross sections perpendicular to the #y#-axis are squares?
The volume is 2.
Let us look at some details.
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To find the volume of the solid with base region bounded by the curve y=1-x^2 and the x-axis if cross sections perpendicular to the y-axis are squares, you can use the method of slicing and integration.
The cross sections perpendicular to the y-axis will be squares with side length equal to the corresponding y-coordinate on the curve.
The volume (V) can be calculated by integrating the area of each square cross section over the range of y-values from 0 to 1 (the range of the curve).
The area of each square cross section is y^2, and integrating this over the range of y-values from 0 to 1 gives the volume:
V = ∫[0 to 1] y^2 dy
After evaluating this definite integral, you'll find the volume of the solid bounded by the curve y=1-x^2, the x-axis, and the cross sections perpendicular to the y-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.
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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