anonymous
  • anonymous
1) A region is bounded by the line y = x and the parabola y = x2 - 6x + 10. What is the volume of the solid generated by revolving the region about the x-axis?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
first we should determine our bounds right?
anonymous
  • anonymous
first draw a rough of a parabola (x^2-6x+10) and dissect it with a diagonal line (y=x). then set x=x^2-6x+10. Solve this it would tell you where parabola and the line intersect.
amistre64
  • amistre64
yep.... or x^2 = -7x +10 (x-5)(x-2)......[2,5]

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amistre64
  • amistre64
well it looked right in me head lol
amistre64
  • amistre64
0 = x^2 -7x +10...better
amistre64
  • amistre64
pi [S] [x^2 -7x +10]^2 dx [2,5] right?
amistre64
  • amistre64
\[F(x) = \pi \int\limits_{2}^{5}[x^2 -7x +10]dx\]
amistre64
  • amistre64
F(5) - F(2) = answer of the volume of the solid formed....
amistre64
  • amistre64
forgot the ^2 in that equation..... there should be an edit button lol
amistre64
  • amistre64
or should we integrate each 'y=' seperately on the interval and then just subtract the higher from the lower?
anonymous
  • anonymous
I think you integrate the given parabola? Must check on this.
anonymous
  • anonymous
Yes you integrate the given function. The other created function is helpful only to create the boundaries.
amistre64
  • amistre64
we tend to get an area shaped like this right? if we find the volume of the solid formed by the y=x in the interval and then subtract the volume of the solid formed by y=x^2 -6x +10...we will end up with the volume of the solid of this area..... and from the last time i messed this up, I recall we had to use pi(y^2) as the intgrands :)
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amistre64
  • amistre64
piR^2 - pir^2 = pi(R^2 - r^2) so we should be able to use the (y=x)^2 - (y=x^2....)^2 as the integrands
amistre64
  • amistre64
but I would feel safer just getting one solid and subtracting the other from it ;)
anonymous
  • anonymous
Sure, If you are a bright student you can do several methods to check, but a non-math major: to find the volume of a solid integrate from a to b, pi*(f(x))^2. (f(x) is given function. Find a, b boundaries as we did above.

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