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Use either a computer algebra system or a table ofintegrals to find the exact length of the arc of the curve$x=\ln \left(1-y^{2}\right)$ that lies between the points $(0,0)$ and$\left(\ln \frac{3}{4}, \frac{1}{2}\right)$

0.599

Calculus 2 / BC

Chapter 7

APPLICATIONS OF INTEGRATION

Section 4

Arc Length

Applications of Integration

Campbell University

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University of Michigan - Ann Arbor

Boston College

Lectures

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Use either a computer alge…

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Find the arc length of the…

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Set up an integral that re…

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Find the exact arc length …

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Express the exact arc leng…

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Use a calculator to approx…

So we have to calculate the length of the okay, and the log given to us is x is equal to l, n, 1 minus y squared okay, and there are y limit here. The yang is from 0 to half tokay in the question we have to calculate using sersokay. So first, let's calculate it first derivative. Let'S differentiate this function with respect to our y, so we can call that x dash as well as will be d x, divided by d y and that will be equals to 1 minus y square. Differentiation of this will be 1 minus y square. Minus 21. Point: okay, so now calculate the length of the length will be the formula: is integration lower limit to upper limit of the upper limit? Here we have as 1 by 2 root over 1 plus first derivative whole square, and this is the first derivative. So that is, if you see this will become 4 y squared divided by 1 minus y square and square of that into b of yon okand if you integrated using the cal system. So it is approximately coming out to the limit l n 3 minus half in and if you calculate this value, that value is approximately 0.5999 point, so that is our answer is crystal. Thank you.

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