CALCULUS

Sketch the region enclosed by the given curves.
y = 4/X
y = 16x, y = 1X/16
x > 0
and the area between the curves

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  1. Can you sketch the curves?

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    👨‍🏫
    bobpursley
  2. yes i just need the area i didn't know how to sketch it on here

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  3. If I read it correctly, you have
    y=4/x, y=16x, and y=x/16 for x>0

    You need to break the area into two regions, because the two top curves intersect at x = 1/2

    So the area is

    ∫[0,1/2] 16x - x/16 dx + ∫[1/2,8] 4/x - x/16 dx
    = (8x^2-x^2/32)[0,1/2] + (4logx-x^2/32)[1/2,8]
    = 255/128 + (4log16 - 255/128)
    = 4log16 = 16log2

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  4. thank you!

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  5. or that's not right

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  6. change the 16log(2) to 16ln(2) and then the answer is correct.

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  7. excellent! thanks a lot!

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