Joy C.

asked • 10/30/20

CALCULUS INTEGRAL NEED HELP ASAP PLEASE THANK YOU!

The formula for the arc length from a to b of a differentiable function is L equals the integral from a to b of the square root of the quantity 1 plus the square of f prime of x dx. Find the length of the curve f(x) from x = 0.5 to x = 1. Your work must show the integral, but you may use your calculator to evaluate it. Give 3 decimal places in your answer.

William W.

What is f(x)?
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10/30/20

Joy C.

I updated the question, the formula should show
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10/30/20

William W.

The formula does show now in your question but this is the generic formula for the length of the arc. In order to solve for the length of the arc specific to this problem, we must know what f(x) is. Take a look at pictures or graphs that may be accompanying the problem to see if f(x) is listed in them. Or perhaps the function f(x) is listed in the header above the problem set.
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10/30/20

Joy C.

I believe the f(x) is "Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. R is the region between the graph of f and the x-axis."
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10/31/20

Joy C.

This was the function in the header and should apply to the 3 questions I posted today.. thank you! sorry for the confusion
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10/31/20

1 Expert Answer

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William W. answered • 10/31/20

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For f(x) = −ln(x), f '(x) = -1/x so the arc length is 0.5 ∫1.0 √(1 + (f '(x))2) dx

0.5 ∫1.0 √(1 + (-1/x)2) dx

0.5 ∫1.0 √(1 + 1/x2) dx


This is a bit of a challenge to get the antiderivative so I plugged it into my calculator and got the arc length = 0.858

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