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find the area the region bounded by the graphs of the given equation y=81x,y=x^5,x=0,x=3

  • calculus -

    The area is between the function y=x^5 and y=81x, between the limits x=0 and x=3.

    The functions are all in the first quadrant (no values negative), and the two curves y=81x and y=x^5 intersect at x=3, the upper integration limit, which is a "lucky coincidence".

    The area function a(x), is therefore
    You would integrate a(x) from 0 to 3 to find the area, thus
    Area = ∫a(x)dx [x=0,3]
    =∫(81x-x^5)dx [x=0,3]

    Here's an image to give you an idea of the area:

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