Examen

ESTEFANIA MENDEZ CAMACHO

1.- Halla tres aproximaciones del área bajo la curva de las funciones siguientes:
a) 𝑥4+2 𝑒𝑛 𝑢𝑛 𝑟𝑎𝑛𝑔𝑜 𝑑𝑒 0 𝑎 5(0)4+2= 2
(1)4+2= (4) + 2 = 6
(2)4+2= 16+2=18
(3)4+2=16+2=18
(4)4+2=256+2=258
(5)4+2=625+2=627

X Y
2 0
6 1
18 2
83 3
258 4
6275

b) −3𝑥3 𝑒𝑛 𝑢𝑛 𝑟𝑎𝑛𝑔𝑜 𝑑𝑒 0 𝑎 5

-3(0)3=0

-3(1)3=-3
-3(2)3=-3(8)=-24
-3(3)3=-3(27)=-81
-3(4)3=64(-3)=-192
-3(5)3=125(-3)=-375

X Y
00
-3 1
-24 2
-81 3
-192 4
-375 5








2.- Halla las integrales de:

a) ∫12𝑥2 𝑑𝑥
= ½ ∫ x2 dx = (1/2)(1/3) x3 + C = 1/6 X3 +C

b) ∫−4𝑥3−9𝑥2+7𝑥 𝑑𝑥
=-4∫x3 dx – 9 ∫x2 dx +7 ∫x dx
=(-4)(1/4) x4 – (9) (1/3) x3 + (7) (1/2) x2 + C
= -X4 -3X3 + 7/2X2 + C

3.- Halla laintegral definida de:

a) ∫𝑥2−1 𝑑𝑥3−3
=∫3-3 x2dx - ∫3-3 dx = 1/3 [x3]3-3 [x]3-3
=1/3 [(3)3 – (-3)3] – [3-(-3)] = 1/3 [27-(-27)] – [3+3]=1/3 [27+27] -6 = 1/3 (54) -6 = 18-6 = 12

b) ∫2𝑥3𝑑𝑥40
=2∫40 x3dx = 2/4 [x4]40 = ½ [(4)4 – (0)4] = ½ [256 – 0] =128

4.- Halla el resultadode:
a) ln5−1
=In (1/5) = In (0.2) = -1.609437

b) 𝑒−4𝑒3
=e-4 e3 = 3-4+3 = e-1 = 0.367879












5.- Halla la integral porsustitución de

a) ∫2𝑥2𝑥3+5𝑑𝑥

u= x3 + 5
du= 3x2 dx
du/3= x2 dx

=2∫x2/x3+5dx=2 ∫du/3/u = 2/3 ∫du/u = 2/3 In | u |+C
= 2/3 In | x3 + 5 | +Cb) ∫−75𝑥−3𝑑𝑥

u = 5x-3
du = 5dx
du/5 = dx
= -7 ∫ dx/5x-3 = -7 ∫ du/5/u = - 7/5 ∫du/u = -7/5 In | u | +C
= - 7/5 In | 5x-3 | +C