Unformatted text preview: e root in the formula for the arc length. The square root makes
evaluating the integral very challenging. Maple is very useful in these calculations, most of which can not be done by using
FTCII because the required antiderivatives are not elementary functions.
For example, in Maple ﬁnd the length of y = sin(x) from x = 0 to x = π .
Since y = sin(x), it follows that dy
dx = cos(x). The length of this curve is then
π 1 + cos(x)2 dx
0 You can use the same int command as you did in Question 1 to compute this integral by entering the following in Maple:
[> restart:
[> int(sqrt(1+cos(x))∧2), x=0..Pi);
The exact value of this integral involves an elliptic function that we will not study in this course. Instead, to get an
approximate value for this integral, use the evalf command as you did before:
[> evalf( int(sqrt(1+cos(x)∧2), x=0..Pi) );
Use Maple’s int command to ﬁnd the exact arc length in each of the following questions and then use the
evalf command to ﬁnd the approximation of the arc length. Submit the printout of your work in Maple
with this assignment.
Question 3(a): Find the length of the curve represented by y = ex from x = 0 to x = 1.
Question 3(b): Find the length of the ellipse represented by 3x2 + y 2 = 3. HINT: Solve for y in terms of x in the ﬁrst
quadrant and set up a deﬁnite integral for the length of that portion of the ellipse. You can then use symmetry to
ﬁnd the total length. iii...
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 Fall '07
 Anoymous
 Antiderivatives, Derivative, Integrals, dx

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