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Integration in solving work

  1. Mar 30, 2009 #1
    1. The problem statement, all variables and given/known data

    can someone please explain to me how to intergrate this:

    the definite integral from 0 to PI of (.25*PI) (1+kh) g (h + .2) dh

    I can leave g, PI, and k in the formula.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 30, 2009 #2
    What have you attempted? Do you know how to integrate polynomials?
     
  4. Mar 30, 2009 #3
    I'm not sure what I need to do. The k is what's causing me problems. I tried factoring but that got me no where. Can you explain what I need to do or explain to me how the book got this answer to this integral? This one of course isn't my problem but can you explain how they intergrated this one? It is similiar to the one I need to solve.


    The definite integral from 0 to 1.5 of (.25 * PI) (1 + kh) g (h + 0.3) dh

    The answer: .366 (k + 1.077) gPI
     
  5. Mar 30, 2009 #4
    Integrate the function with respect to h and then insert the upper value of the integral for h and then do the same for the lower value of the integral and subtract the two.
     
  6. Mar 30, 2009 #5
    Remember that constants come outside the integral.
     
  7. Mar 30, 2009 #6
    Ok so I can pull out PI, g, and .25? Or just PI and g?

    And do i distribute (1 + kh) * (h + .2)???
     
  8. Mar 30, 2009 #7
    Is k a constant (A number which does not depend on the variable of integration h)? If so, remember this rule of integration of two integrable functions f and g:
    [tex]\int (f + g) = \int f + \int g[/tex]
    and if k is a constant:
    [tex]\int kf = k\int f[/tex]
    Also, remember the power rule of differentiation:
    [tex]\frac{d}{dx}(x^n) = nx^{n-1}[/tex]
    from which we get:
    [tex]\int x^n dx = \frac{x^{n+1}}{n+1} + C[/tex]
    where C is an arbitrary constant of integration.
    The best course of action is then to multiply everything out so that you are left with a polynomial, where you can integrate each term in the sum separately.
     
  9. Mar 30, 2009 #8
    So I'm getting...

    .25*PI*g * (The definite integral from 0 to 1.5 of (h + kh^2 + .2 + .2kh).

    I don't know what to do with this k.

    If I integrate I'm getting

    .25*PI*g * { (h^2/2) + ((kh^3)/(3)) + (.2h) + (.1k*h^2)} evaluated from 0 to 1.5
     
  10. Mar 30, 2009 #9

    Redbelly98

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    Looks good, now just evaluate it with the limits 0 to 1.5.
     
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