What area does the antiderivative represent?Consider the antiderivative of the function e − x ,, which is − e − x .. Evaluating the antiderivative at the value 0 produces -1.I was taught to conceptualize an antiderivative as an area under a curve, or a sum of progressively smaller approximate sections.But clearly, -1 cannot represent the area under under the e − x curve from 0 to 0, 0 to ∞, or − ∞ to 0 when you consider that the function is positive for all values of x.Then what sum or area does the value of the antiderivative of e − x actually represent?

Question

What area does the antiderivative represent?Consider the antiderivative of the function       e          −      x        ,, which is   −      e          −      x        .. Evaluating the antiderivative at the value 0 produces -1.I was taught to conceptualize an antiderivative as an area under a curve, or a sum of progressively smaller approximate sections.But clearly, -1 cannot represent the area under under the       e          −      x       curve from 0 to 0, 0 to   ∞, or   −  ∞ to 0 when you consider that the function is positive for all values of x.Then what sum or area does the value of the antiderivative of       e          −      x       actually represent?

Reagan Madden · Accepted Answer

Explanation:Evaluating the antiderivative at the value 0 produces −1. Now, I was taught to conceptualize an antiderivative as an area under a curve1. An antiderivative F results from performing indefinite integration on a function f.2. For   a  &amp;lt;  b  ,, the signed area (i.e., the area residing in the positive vertical region minus the area residing in the negative vertical region) enclosed by the curve   y  =  f  (  x  )  ,, the x-axis, and the lines   x  =  a and   x  =  b is given by the definite integral       ∫    a    b    f  .3. By the Fundamental Theorem of Calculus, the above signed area       ∫    a    b    f  =  F  (  b  )  −  F  (  a  )  .4. The actual area enclosed by the curve   y  =  f  (  x  )  ,, the x-axis, and the lines   x  =  a and   x  =  b is given by       ∫    a    b        |    f      |    ,, which does not equal   F  (  b  )  −  F  (  a  )  .5. In your Question, the value evaluation   F  (  0  )  =  −  1 does not correspond to an area.

What area does the antiderivative represent? Consider the antiderivative of the function

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