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Math Help - Final exam tomorrow, need help!

  1. #1
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    Final exam tomorrow, need help!

    I don't need any work shown I just need the answers so I can check my answer. I have my final exam tomorrow so I need to be sure I'm doing these right.

    Any answer would help me out a lot, but the more I can get answers to the better.

    Thanks so much!

    a) Initial value problem
    dy/dx=y^2 + 1
    y(4)=0

    b)Find the area of the surface obtained by rotating the curve about the y-axis?

    y=(1/4)*x^2 - (1/2)*ln(x); 1≤x≤2

    c)Find the length of the curve

    x=((y^4)/8) + (1/(4*y^2)); 1≤y≤2

    d)Solve the differential equation.

    7yy' = 5x

    e)Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis.

    y=e^x; 1≤y≤3; y-axis

    f) Find the area of the surface obtained by rotating the curve about the x-axis.

    x= (1/3)*(y^2 +2)^(3/2)
    1≤y≤3

    g)Find the area of the surface obtained by rotating the curve about the x-axis.

    y=x^3
    0≤x≤3
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  2. #2
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    Have you made any attempts at these or are we working with a blank canvas? Showing some working will help us help you.


    Quote Originally Posted by DanS29 View Post
    a) Initial value problem
    dy/dx=y^2 + 1
    y(4)=0
    This first one is separable.

    \frac{dy}{dx}= y^2 + 1

    \frac{dy}{ y^2 + 1}= dx

    Now integrate both sides, after you show me that, I will show you more.
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  3. #3
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    a
    y=tan(x-4)

    d
    y=\pm\frac{1}{7}\sqrt{35x^2+49C}
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by DanS29 View Post
    I don't need any work shown I just need the answers so I can check my answer. I have my final exam tomorrow so I need to be sure I'm doing these right.

    Any answer would help me out a lot, but the more I can get answers to the better.

    Thanks so much!

    a) Initial value problem
    dy/dx=y^2 + 1
    y(4)=0

    b)Find the area of the surface obtained by rotating the curve about the y-axis?

    y=(1/4)*x^2 - (1/2)*ln(x); 1≤x≤2

    c)Find the length of the curve

    x=((y^4)/8) + (1/(4*y^2)); 1≤y≤2

    d)Solve the differential equation.

    7yy' = 5x

    e)Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve about the given axis.

    y=e^x; 1≤y≤3; y-axis

    f) Find the area of the surface obtained by rotating the curve about the x-axis.

    x= (1/3)*(y^2 +2)^(3/2)
    1≤y≤3

    g)Find the area of the surface obtained by rotating the curve about the x-axis.

    y=x^3
    0≤x≤3
    Damn! thats too many questions... it is hard to read.. it would be great if you posted the questions separately

    for no.c to find the length of the curve:

    first find out the derivative of the given funciton...and then the length of the curve is given by

    L =\int_1^2 \sqrt {1+ \mbox{(derivative)}^2} \mbox{dy}

    you can check your answers for differentiation, integration etc. at this website
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