Help with volume of revolution questions Watch

swifty
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#1
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Hi I am stuck with two questions:

1) The area enclosed by the curve y = x^3 + 1, the x-axis and the line x=1.

I know volume = Pi X the intergration of (y2) and filling in the points X=1 and X=0 but i'm not getting the correct answer.....

2) The area enclosed by the curve y = 4x - x^2 and the x-axis. But where is the second x value? When I intergrate do I not have to fill in two values of X?

Thanks very much :tsr2:
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swifty
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Hi thanks for helping, for question 1 I got the same answer as you but the answer is 16Pi/7....
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dvs
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I believe the answer is correct. It asked for the volume of the area enclosed by the curve and the x-axis. So you have to integrate over the interval [-1, 1], and not [0, 1].
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Christophicus
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(Original post by e-unit)
The answer is wrong.
Ha ha. :p:
y = x^3 + 1 => y^2 = (x^3+1)^2 = x^6+2x^3+1

VOLUME = pi(x^7/7 + x^4/2 + x) between x = -1 and x = 1
VOLUME = pi(1/7+1/2+1) - pi(-1/7+1/2-1)
VOLUME = 16pi/7
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meef cheese
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(Original post by swifty)

1) The area enclosed by the curve y = x^3 + 1, the x-axis and the line x=1.
Ha ha.
y = x^3 + 1 => y^2 = (x^3+1)^2 = x^6+2x^3+1

VOLUME = pi(x^7/7 + x^4/2 + x) between x = -1 and x = 1
VOLUME = pi(1/7+1/2+1) - pi(-1/7+1/2-1)
VOLUME = 16pi/7
Le sigh.

I would neg rep you back, but I usually quite like you - you're normally helpful and intelligent.
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Christophicus
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(Original post by e-unit)
Le sigh.

I would neg rep you back, but I usually quite like you - you're normally helpful and intelligent.
Yh sorry dude about the neg rep. I just believe that you can be passionate about a subject without achieving the top grades. My mechanics teacher who knows M1-M6 and C1-FP3 like the back of his hand got a B at a-level. Does that mean he hates maths or isn't passionate enough? I think the fact he got a 1st in his maths degree and carried on a phd in maths is enough evidence that he's passionate!
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swifty
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Hi Widowmaker could you explain to me why you used the value X=-1 and X=1? Even though it said the x-axis and the line x=1?

Thank you!
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Geminus
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(Original post by swifty)
Hi Widowmaker could you explain to me why you used the value X=-1 and X=1? Even though it said the x-axis and the line x=1?

Thank you!
It's because the curve crosses the x axis at -1. Set the equation equal to 0 and then you can see where the curve crosses the x axis; hence this is the area bounded by the curve and the x-axis. If that makes sense!
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