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Couple of simple (I hope) questions

  1. Aug 17, 2009 #1
    1. The problem statement, all variables and given/known data

    1st problem

    I'm struggling to answer this question using my calculus workbook.

    Find the point of intersection of the lines:

    [tex]y_{1}=3x+2[/tex]
    [tex]3y_{2}=16-x[/tex]

    I can solve this question as a simultaneous equation, but, as it is in my calculus question paper believe it to be less simple. Is there some method of differentiating the equations in order to work out the intersect point?

    2nd problem

    If [tex]f(x)=7x^3 + 8x^2 - x + 11[/tex], evaluate;

    a) [tex]\int\stackrel{+1}{-1}f(x)dx[/tex]

    b) [tex]\int\stackrel{+1}{-1}f ' (x)dx[/tex]

    c) [tex]\int\stackrel{+1}{-1}f '' (x)dx[/tex]

    I'm happy with the integration but just wanted to make sure that I am working the integration of first the function, then the higher order derivatives or should it be higher order integration.

    Sorry if the problems seem simple but I'm struggling to understand my workbook.
     
  2. jcsd
  3. Aug 17, 2009 #2
    Your first exercise is just a system of simultaneous equations as you suspected. Differentiation is not needed (and wouldn't help as two functions with equal derivative are not necessarily equal).

    The second problem is simpler than it might appear. The problem deals with integrals of higher-order derivative. The Fundamental Theorem of Calculus gives you a handle on this one.

    [tex]\text{If } F'(x) = f(x) \text{ then } \int{f(x)\;{dx}} = F(x) + C[/tex]

    --Elucidus
     
  4. Aug 17, 2009 #3
    Thanks for the reply.

    Happy with the first part.

    But for the 2nd. Are you saying that I have carried it out incorrectly by findging the first and second derivative and then integrating them and working out thorugh the boundary values?
     
  5. Aug 17, 2009 #4
    I am saying that [itex]\int_{-1}^1 f'(x)\;dx=f(1)-f(-1)[/itex] since f(x) is an antiderivative of f'(x). Patern continues...

    --Elucidus
     
  6. Aug 18, 2009 #5
    Thanks for your help. I reckon I have it sorted now.

    Cheers
     
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