Ejercicios De Integral Definida

EJERCICIOS DE INTEGRAL DEFINIDA
1. 027dx =7x02
=72-70
= 7
2. 24(1-e)dx = (1-e)x24

3. 125x dx =125x22
=5x2212
=5(2)22- 5(1)22
=10-52
= 152
4. 05-3x dx =-3x2205
=-3 (5) 22-3(0)22
=-3(25)2
=-752
5. -31(2x-3)dx =-312xdx--313 dx
=2x22-3x-31
=1-3-9+9
= - 20
6. -114-9ydy =4y-9y22-11=4y-92y2-4y-92y2-11
=4(1)-92(1)2-4-1-92(-1)2
=4-92--4-92
=8-92--8-92
=-12--172 = -1+172 = 162= 8

7. 23y2-2y+1 dy =y33-2y22+y23
=333-(3)2+3-(2)33-22+2
=273-9+3-83-4+2
=3-23 = 9-23= 73
8. 322+t2dt =322t-32t2dx
= 2t22-t3332
=t2-t3332
=4-83-9-9
=12-83-9+9= 43
9. -2-13w2-w-1dw =-2-13w2--2-1w--2-1dw
=3w33-w22-w-2-1
=-1-12+1--8-12+2
=12+92=1+92=82=4
10. 89dt= t-t89
=9-8=1
11. 12-4t4dt= -4t-3-312
= 43(2)-3-43(1)-3
= 43 18-43
=16-43= 1-86=-76
12. 12(x)-22dx=1212x-2dx
= 12 x-1-112
= -12x-112
= -12(2)-1--12(1)-1
= 14+12=-1+24=14
13. -113x5dx = -11x53dx
= x8383-11
= 38x83-11
=38(1)83-38(1)83=0
14. 1232(x2+x+1)dx = x33+x22+x1232
= 3233+3222+32-1233+1222+12
= 27831+9421+32-1831+1421+12
= 98+98+32-124+18+12
= 9+9+128-1+3+1224
= 308-1624= 154-23=45-812=3712
15. 1231x2dx = 133x-2dx
= x-1123
= (3)-1-12-1
= 13-2=1-63=-53
16. 491x-2dx = 49(x)-12-2dx
= x1212-2x49
=29-2(9)-24-2(4)
=6-8-4-8=-12+4=-8
17. -11(z+1)5dz = -11z5+z4+z3+z2+z+1dz
= z66+z55+z44+z33+z22+z-11
= 16+16+14+13+12+1-16-15+14-13+12-1
= 10+12+15+20+30+6060-10-12+15-20+3060= 14760+3460=18460=435
18. 18x13-x-13dx = x4343-x232318
= 34(8)43-43(1)43-23(1)23
= 34(16)-32(4)-3-64 = 2-6-34= 274
19. 012x2(x3-1)3 = 012x11-6x4+6x3-2x2 dx
= 2x1212-6x55+6x44-2x3301
=212-65-64-23=360-72+90-4060=16930
20. 13(x+3)3dx = 13x3+9x2+27x+27dx
= x44+9x33+27 x13
= (3)44+3(3)3+27222+27(3) -(1)44+3(1)3+27(1)22-27(1)
= 81+324+486+3244-1+12+27+1084
= 12154-1484=10674
21. 184ydy= 1841ydy = 4lny
=4ln8-4ln1=8.317
22. -(ex)-1 6xdx= -(ex)-1 61xdx
=6lnx-(ex)-1
=6ln-1-6ln-ex=-6
23. 01e5dx=
24. 0e-11x+1dx=
25. 02x2ex3dx= 02x2eudu3x2 u=x3= 02eu3du u=3x2
= 13eu02 du3x2=dx
= 13ex302
= 13e2-13e0=993.22u2
26. 013x2+4x(x3+2x2)4dx = 013x2+4x(u)4dx u=x3+2x2
= 013x2u4+4xu4 u=3x2+4x
= 01u4du=u55 du3x2+4x=dx
= (3x2+4x)5501 =(312+4(1))55-0
= (3+4)55=168075=3361.4
27. 452(x-3)3dx=452(x-3)-3dxu=x-3
= 452(u)-3du du=dx
=u-2=1(x-3)2
= 1(5-3)2-14-32=14
28. 062x+4dx = 06(2x+4)12dx u=2x+4
= 06(u)122du= 12 u3232 du2=dx
= 13u32=13(2x+4)32
= 13(2(6)+4)32-13(2(0)+4)32
= 1364-138=643-83=563
29. 13210-3pdp=132(u)-12du3
= -13u3232
= -2910-3p32- -2910-3p32
= -2910-3(2)32- -2910-31332
= -298+2927=-169+6=-16+579=389
30.-11qq2+3dq=-11q(u)-12du2q
= 12u3232=12(q2+3)32-12(q2+3)32
= 138-1328=1.78
31. 01x237x3+1dx=01x2(u)13du2x
= u4343=347(1)3+1 73-341 73
=12-34=484
32. 072x-x(x2+1)53=072x-x(x2+1)-53 u=x2+1
= 072x-x(u)-53du2x u=2x
=2x2x-u23-23 dx=du2x
= 7+23(7)-23-1=3.36
33. abm+nydy=my+ny22
=mb+n(b)22-ma+n2(a)2
=mb+nb22-ma+na22
34.01ex-e-2xdx=01ex-eudu2 u=-2x
= ex+12eu=ex+12e-2x dx=-du2
=e1+12e-21-e0+12e0=11.87-1.5=10.37
35. -218xdx=-218x22=-214x2
= 4x2-4x2
= 4(1)2-4(-2)2
= 4-16=12
36. 1e2x-1+x-2-x-3dx=-1e21-x-1+x-22
= 21-e-1+e-22-1-(1)-1-(1)-22
37. 126x-12xdx=126(x)12-2(x)12
= 6x3232-2x3232
= 4x32-2(2)x323
= 4x32-0.94x32...