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Math Help - Utter confusion over a simple question

  1. #1
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    Utter confusion over a simple question

    So the question is:


    If f(x) is the slope of a walking track at a distance of x kilometres from the start of the track, what does
    \int_3^5f(x)dx represent?


    So, yeah, Im confused as to what the answer is. Solving that out would give a value right. And the value would be the area under the curve. Is it something to do with the total change of the slope from 3km from the start to 5km? Or am I completely off?

    I'm sure this is really simple, but nonetheless, I am more lost than the people on the show LOST.
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  2. #2
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    Quote Originally Posted by Johnaloa View Post
    So the question is:


    If f(x) is the slope of a walking track at a distance of x kilometres from the start of the track, what does
    \int_3^5f(x)dx represent?


    So, yeah, Im confused as to what the answer is. Solving that out would give a value right. And the value would be the area under the curve. Is it something to do with the total change of the slope from 3km from the start to 5km? Or am I completely off?

    I'm sure this is really simple, but nonetheless, I am more lost than the people on the show LOST.
    Let y = y(x) be the height of the track above an arbitrary horizontal line (the x-axis). Then f(x) = dy/dx. So it looks to me like the integral is equal to y(5) - y(3), which would represent the difference in height of the track at those two points ......
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