-
1. F (a) = A F (b) - .sin (8x 5)dx a = 5
8; b = 1;A = 1
8,
2. F (a) = A F (b) - . 3arccos2 x1 x2 dx a = 1; b = 0;A = 1,
3. F (a) = A F (b) - .(x2 + x) cosxdx a = 0; b = pi;A = 3,
4. , F (a) = A F (b) .xdx
2 +x+ 4
a = 1, b = 0, A = 2
3,
5. , F (a) = A F (b) .2 tanx+ 3
sin2 x+ 2 cos2 xdx a =
pi
4, b = 0, A = ln 3 +
32arctg
12
+ 1,
6. .
43
x2dx
x2 6x+ 10 ,
7. .
0
xdx4
(16 + x2)5,
8. D .
D : y2 = 4x, x =8
(y2 + 4),
9. .{x = 4(cos t+ t sin t)y = 4(sin t t cos t) 0 t 2
10. .
z =4xy
x 3y + 1(a) x 3y + 1 < 0 (b) x 3y + 1 0 (c) x 3y 1 0 (d) x 3y
+ 1 6= 0
(e) x 3y + 1 > 0 (f) x 3y 1 0 (g) x 3y + 1 0 (h) x 3y1 6=
0
11. zx(a, b) zy(c, d) .
z = arccosy
xc = 5; d = 3, zy(c, d) =?
-
12. u(x, y) C = 0 u(M) - .exy(1 + x+ y) dx+ exy(1 x y) dy, M =
(e, e)
13. z = z(x, y) zx .
x2 + y2 + z2 + 2xy yz 4x 3y z = 0 = 2, M0(1,1, 1)
14. z = z(x, y) D .
z = 3x2 + 3y2 x y + 1, D : x = 5, y = 0, x y 1 = 0
15. f(x, y, z) g(x, y, z) = 0 - .
2x+y+3z = 9 3x+2y+z = 6 .
16. .
n=1
3
9n2 3n 2
17. .( 1- ,
0- . )
n=1
(arcsin
1
3n
)2n
18. .
n=1
(0.1)nx2n
n
19. , .
n=1
(2n+ 3)x2n
(n+ 1)5
20. f(x) , .
f(x) =
{ x, pi x 0x2/pi, 0 < x pi ,
n=1
3 (1)nn2
21.
a2 .
12: 21- .
-
22. .D
(xy2) dxdy, D : y = x, y = 0, x = 1
23. .V
x2sh(2xy)dxdydz;V : x = 1, y = 0, y = x, z = 0, z = 8
24. .
RR
0R2x2
sinx2 + y2
x2 + y2dy dx
25. .
.
(x2 + y2)2 = a2(4x2 + y2), a = 2
26. .
z = x2, x 2y + 2 = 0, x+ y 7 = 0, z 0
27. D .a = 2D : x2+y22ay 0, x2+y22ax 0, y 0, OY
28. .
L
F1dx+ F2dy + F3dz
F = (xy, yx), L : y2 = x O(0, 0) A(1, 1) .
29.
L
(x, y, z) dl .
(x, y, z) = x2+y2+z2, L : x = a cos t, y = a sin t, z = bt, 0 t
2pi.
30. .
~F = xy (x, y), D = {(x, y)|1 x2 + y2 4 }
