   Chapter 10.1, Problem 81E

Chapter
Section
Textbook Problem

# Arc Length Use the integration capabilities of a graphing utility to approximate to two-decimal-place accuracy the elliptical integral representing the circumference of the ellipse x 2 25 + y 2 49 = 1 .

To determine
The arc length of the provided ellipse x225+y249=1 with the help of graphing utility.

Explanation

Given:

The equation of ellipse x225+y249=1.

Formula used:

The arc length of an ellipse, x2a2+y2b2=1 is formulated as 4a0π21e2sin2θdθ where e2=a2b2a2.

Calculation:

Consider the equation of the ellipse, x225+y249=1.

Compare the provided equation x225+y249=1 with the standard equation of ellipse x2b2+y2a2=1. Here, it is observed that the provided ellipse has the ordinate as the major axis..

So, it is clear from the provided equation that b=5 and a=7.

Now, calculate the eccentricity e for the ellipse, x225+y249=1 which is formulated as, e2=a2b2a2.

Substitute b=5 and a=7 in the equation, e2=a2b2a2

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