Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

160 Definite Integrals [Ch. 5
Example 3. Find the length of the entire curve r = asin-|- (Fig. 51).
The entire curve is described by a point as cp ranges
Solution. We have r' = a sin 2
She curve is
Fig. 51
from to 3ji.
-^- cos , therefore the entire arc length of
o o
8JI 8JI
s=
J J/a* sin
-| +o sin* cos' d . =^
1665. Compute the arc length of the semicubical parabola
y* = x* from the coordinate origin to the point x = 4.
1666*. Find the length of the catenary y = acosh-^- from the
vertex A (6,a) to the point B(b,h).
1667. Compute the arc length of the parabola y = 2}/"x from
x=0 to x=l.
1668. Find the arc length of the curve y = e* lying between
the points (0,1) and (l,e).
1669. Find the arc length of the curve y = lnx from x = /3
to *=K8.
1670. Find the arc length of the curve y = arc sin (e~*) from
* = to jc=l.
1671. Compute the arc length of the curve x = In secy, lying
between = t/ and = j/ -5- .
o
2
1672. Find the arc length of the curve x =
^-y
= e.
=1 to
-^\ny from