Kehlani F.

asked • 01/15/20

I need help with integral please!

Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 - x2 and the x-axis?

Options:

  1. the integral from 0 to 1 of the quantity 1 minus x squared, dx plus the integral from 1 to 2 of the quantity 1 minus x square, dx
  2. the integral from 0 to 1 of the quantity 1 minus x squared, dx minus the integral from 1 to 2 of the quantity 1 minus x square, dx
  3. the integral from 0 to 2 of the quantity 1 minus x squared, dx
  4. 2 times the integral from 0 to 1 of the quantity 1 minus x squared, dx

1 Expert Answer

By:

Mark H. answered • 01/15/20

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First, sketch the graph of the function. You have a parabola that opens down with roots at x = 1, and -1

I would have said to integrate from x = -1 to x = +1, but I think answer #4 is the same thing.


Use your graph as a "sanity check"--looking at my graph, it looks like the answer is approx. 1.2

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