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Math Help - Urgent!!! disk and washer method

  1. #1
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    Urgent!!! disk and washer method

    I can't get these 4 problems. I just don't get how to do them. I had a sub today in math and my teacher had us learn the chapter ourselves and do it but i can't get these answers. Help w/ explaining would highly be appreciated!!! I don't care if you only do one or two, i just need to grasp the subject. 1. find the volume of the solid bounded by these equations about the indicated lines. equations: y=square root of (x) y=0 x=4. About the line x=6. 2. sames as above: equations y=2x^2 y=0 x=2 about the line y=8.

    3. same above : y=6-x y=0 y=4 x=0 about the line x=6.
    4. y=x * square root of (4-x^2) about y=0.

    Please Hurry!!! thanks in advance and i will be waiting here trying to figure them out Thanks!!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    ok

    The fourth one is just a basic one you need to use the formula V=pi* \int_a^{b}R(x)^2-r(x)^2dx\...so you see that you need to find the zeros of x(4-x^2)^{\frac{1}{2}}\ so either x=0 or (4-x^2)^{\frac{1}{2}}\=0 so x=0 or x= \pm2 by graphing you will see that you need to set up two integrals since [-2,0] the graph is below the x-axis and from [0,2] its above so what you do is apply the formula v=pi* \int_a^bR(x)^2-r(x)^2dx\ so V in this case is equal to pi* \int_{-2}^{0}0-x(4-x^2)^{\frac{1}{2}}dx\+pi* \int_0^{2}x(4-x^2)^{\frac{1}{2}}-0,dx\=well I will leave that up to you

    the other ones when you revolve it around a vertical axis I'd use shell method which is V=2 pi\ \int_a^{b}h(x)g(x)dx\ where h(x) is the the distance from the axis to any point in the region you are revolving and g(x) is your curve
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  3. #3
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    thanks but for 4. shouldn't you square the equation. i got 128 pi /15 for that
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Haha

    Wow yes you aer right I suck so follow everything I said except it should now be [x(4-x^2)^{\frac{1}{2}}]^2\ in each integral..and that simplifies to 4x^2-x^4\...which then integrates to \frac{4}{3}x^3-\frac{1}{5}x^5\..haha sorry about that lol
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  5. #5
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    i don't get your other formula with h(x)g(x) i don't think we've learned that yet. What i did was move the equation over for example if it was square root of (x) and it said revolve around x=4 i'd add four so it moved the equation back 4 and then revolved around the y for the answer.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    If you are going to do it

    without the shell method you have to solve the equation so that it is no longer a function of x but now a function of y and use v=pi* \int_c^d{R(y)^2}dy
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  7. #7
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    no i knew that but i was asking if there's an easier way
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  8. #8
    MHF Contributor Mathstud28's Avatar
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    Ok

    no there is not withou the shell method...occasionally there are little teensy short cuts such as \int_{-a}^{a}f(x),dx=2 \int_0^{a}f(x).dx when f(x) is an even function but no...its really just that hard at your level...sorry
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  9. #9
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    so my ways the only way ...so far?
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  10. #10
    MHF Contributor Mathstud28's Avatar
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    yes

    Unfortunately it is....you should learn an easier way...or Triple integrals ...jk...just sit tight and do it the long way...it will come eventually
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  11. #11
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    alright thanks bud, i really appreciate it. Finally finished see ya
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  12. #12
    MHF Contributor Mathstud28's Avatar
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    Hah

    no problem...Im always here if you need help!o and good job for finishing
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