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

Sec. 7\_The Areas of Plane Figures__157
1639. Find the area of the figure bounded by the hyperbola
~ f2 = l and the straight linex = 2a.
1640*. Find the entire area bounded by
1641. Find the area between the catenary
y = a cosh ,
2
the (/-axis and the straight line = f/ ~(e + !)
the astroid
1642. Find the area bounded by the curve a*y* = x 2
(a*
1643. Compute
the area contained within the curve
2
;c
).
1644. Find the area between the equilateral hyperbola x* y* ~
= 9, the x-axis and the diameter passing through the point (5,4).
1645. Find the area between the curve y ~i, the x-axis,
and the ordinate x=l (x>l).
X 9
1646*. Find the area bounded by the cissoid 2 = J yr/ o2ax
and its asymptote x = 2a (a>0).
1647*. Find the area between the strophoid y* = x ( x ~~ a)2 and
2Jfl^~~ X
its asymptote (a>0).
1648. Compute the area of the two parts
2
circle jt
2
+ r/ =--8 is divided by the parabola if =2x.
into which the
2
1649. Compute the area contained between the circle x + y 2 = 16
and the parabola x*=l2(y 1).
1650. Find the area contained within the astroid
jc = acos 8
8
/; y= b sin /.
1651. Find the area bounded by the x-axis and one arc of
the cycloid
f x = a(t sin/),
\ # = a(l cos/).
1652. Find the area bounded by one branch of the trochoid
tefr***/-