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A couple of integration problems

  1. Apr 1, 2012 #1
    1. The problem statement, all variables and given/known data
    a) S(4 is higher limit, 0 is lower limit) (x^4 - x^2 + 1)dx

    b) S(pi is higher limit, -pi is lower limit) (cosx + sinx)dx


    2. Relevant equations

    The S is the integration sign

    3. The attempt at a solution

    a) = ((x^5)/5)-((x^3)/3)+x I(4 high, 0 low)

    = (((4^5)/5)-((4^3)/3)+4)-(0)

    Is this the final solution or is there another step i don't know about?

    b) = (sinx + -cosx) dx I(pi high, -pi low)
    = (sin(pi)-cos(pi))-(sin(-pi)-cos(-pi))

    Is this the final solution?
     
  2. jcsd
  3. Apr 1, 2012 #2

    LCKurtz

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    While your answers are technically correct, you should simplify them both. Put in the values of ##\cos \pi## and ##\sin \pi##.
     
  4. Apr 1, 2012 #3
    so basically:

    (0-1)-(0-1)?
     
  5. Apr 1, 2012 #4

    LCKurtz

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    You consider that simplified? What's your final answer?
     
  6. Apr 1, 2012 #5
    0 right
     
  7. Apr 1, 2012 #6
    do I simplify the first one aswell? Cause someone said I didn't have to.
     
  8. Apr 1, 2012 #7

    LCKurtz

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    0 is the correct answer, but I'm not sure you didn't make a couple of cancelling arithmetic mistakes along the way. In post #3 it appears you made the following step:

    (sin(pi)-cos(pi))-(sin(-pi)-cos(-pi))
    = (0-1)-(0-1)

    The arithmetic in that step has two errors. With regard to your first one, I wouldn't consider it simplified until it is a single fraction reduced to lowest terms.
     
  9. Apr 1, 2012 #8
    I'm not following. What do you mean reduced to lowest terms?
     
  10. Apr 1, 2012 #9

    LCKurtz

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    (((4^5)/5)-((4^3)/3)+4)-(0)

    I mean combine the three terms into a single fraction; get rid of all those parentheses.

    A fraction is reduced to lowest terms when the numerator and denominator have no common factors. For example, you wouldn't leave an answer as ##\frac{42}{30}## when it could be reduced to ##\frac{7}{5}##.
     
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