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

Sec. 1] The Double Integral in Rectangular Coordinates 249*
2127. S is a rectangle with vertices 0(0, 0), 4(2,0), 5(2, 1),
C(0, 1).
2128. S is a triangle with vertices 0(0, 0), 4(1, 0), 5(1, 1).
2129. S is a trapezoid with vertices 0(0, 0), A (2, 0), 5(1, 1),
C(0, 1).
2130. S is a parallelogram with vertices 4(1, 2), 5(2, 4),
C(2, 7), D(l, 5).
2131. S is a circular sector 045 with centre at the point
(0, 0), whose arc end-points are A (1, 1) and 5 f - 1, 1) (Fig. 88).
Fig 89
2132. S is a right parabolic segment 405 bounded by the
parabola 504 and a segment of the straight line 54 connecting
the points 5(~-l, 2) and 4(1, 2) (Fig. 89).
2133. S is a circular ring bounded by circles with radii r=l
and /?-=2 and with common centre 0(0, 0).
x 2
2134. S is bounded by the hyperbola if x? \ and the circle
2
| // ^9 (the region containing the origin is meant).
2135. Set up the limits of integration in the double integral
(S)
(x, y)dxdy
if the region S is defined by the inequalities
b) * 2
h// 2