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11.1 Finding Area Under a Curve

Finding Area Under a Curve

  • Integration, or in exact definite integrals, are useful in finding areas under a graph.
  • In this course, the total area is more of a concern compared to the signed area, if the questions requests you to find an area of a region. Therefore, it can be found using definite integrals as above, but be mindful of whether the area is above the x-axis, below, or mixed.
  • In the following, consider the function f(x) and the area A of the region contained by the curve, the axis and the range x\in[a,b].

i) If f(x)\geq0 for all x\in[a,b], then we have

A=\int_{a}^{b} f(x) d x

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