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

156__Definite Integrals_[Ch. 5
Solution. By virtue of the symmetry of the curve we determine first one
quadrant of the sought-for area:
Whence S = a 2 .
1623. Compute the area bounded by the parabola y = 4x x z
and the x-axis.
1624. Compute the area bounded by the curve y = \nx, the
;t-axis and the straight line x = e.
1625*. Find the area bounded by the curve y x (x 1) (* 2)
and the x-axis.
1626. Find the area bounded by the curve y* = x, the straight
line y=l and the vertical line x = 8.
1627. Compute the area bounded by a single half-wave of the
sinusoidal curve y=smx and the Jt-axis.
1628. Compute the area contained between the curve y = ianx,
the x-axis and the straight line x = ~ .
1629. Find the area contained between the hyperbola xy = m*,
the vertical lines x^a and x = 3a (a>0) and the x-axis.
1630. Find the area contained between the witch of Agnesi
u= - and the x-axis.
y x 2 + a 2
1631. Compute the area of the figure bounded by the curve
y~x*, the straight line y = 8 and the y-axis.
1632. Find the area bounded by the parabolas y**=2px and
x 2 = 2py.
1633. Evaluate the area bounded by the parabola y = 2x x*
and the straight line = f/ x.
1634. Compute the area of a segment cut off by the straight
line y = 3 2x from the parabola y = x 2
.
1635. Compute the area contained between the parabolas y*=*x*,
*/=Y and the straight line y = 2x.
1636. Compute the area contained between the parabolas
y = and y = 4 |x 2
.
1637. Compute the area contained between the witch of
1
x z
Agnesi y = and the parabola f^.
1638. Compute the area bounded by the curves y**e*>
and the straight line x=l.