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I'm having problems trying to figure this out please help.
the equation is y=1-X^2 and you must slice with squares and they must be perpendicular to the y-axis.
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it says to integrate and find volume
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hi Double
Welcome to the forum.
Sketch the graph and draw two horizontal lines close together from the y axis to the curve, so you have drawn a typical strip. This strip has area x across and dy width. If you were asked for the area of the part of the curve between y = 0 and y = 1 you would add up the strips like this:
You cannot integrate a function of x with respect to y, so you need to substitute with
The resulting function is directly integrable.
But you ask for a volume, so I'll assume this means that the area is rotated around the y axis to create a solid 'volume of revolution'.
Go back to the original strip and imagine it rotates around the y axis so as to generate a thin disc. The area of this disc is π x^2 ( ie. pi radius squared ) and so its volume is π x^2 .dy Here the new integral:
Once again you need to replace the function of x with one involving y ....... x^2 = 1 - y
So we then end up with this integral:
Can you finish from here?
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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Hey thank you for the help, and you are correct it was the volume of revolution I got that exact setup and got 1/2 unit^3 but I forgot to add the pi like always thank you for the help!
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