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March 25, 2017

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Find the areas of the regions bounded by the lines and curves by expressing x as a function of y and integrating with respect to y.

x = (y-1)² - 1, x = (y-1)² + 1 from y=0 to y=2.

I graphed the two functions and the do not intersect? Does it matter? Or do I still find the area in between?

Thank you!

  • Calc - ,

    You're right, unless you have made a typo, the two curves will never intersect.

    As you said, it does not matter, the lines y=0 and y=2 will intersect both lines to make a curved rectangle whose area you'd have to calculate. The result should be a nice integer.

  • Calc - ,

    Even though they don't intersect, there is the area bounded between y=0 and y=2

    Did you notice that the two parabolas are congruent and the second is merely translated 2 units to the right?
    so the horizontal distance between corresponding points is always 2

    that is x2-x1 = (y-1)^2 + 1 - ((x-1)^2 - 1) = 2

    Area = ∫x dy from 0 to 2
    = ∫ 2dy from 0 to 2
    = [2y] from 0 to 2
    = 4-0 = 4

    check my thinking, seems too easy.

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