Unidad 4 Tarea 1

Ulises Morales

May 31, 2015

1 Ejercicio:

f(x) = ln((

4x)) + 2x , [0 ; 2] , n= 20 rectangulos

2 Solucion:

base = 2020

= 0.1

3 Calculando F(x):

f(0.1) = ln((

4(0.1))) + 2(0.1) = 0.258

f(0.2) = ln((

4(0.2))) + 2(0.2) = 0.2884

f(0.3) = ln((

4(0.3))) + 2(0.3) = 0.6911

f(0.4) = ln((

4(0.4))) + 2(0.4) = 1.035

f(0.5) = ln((

4(0.5))) + 2(0.5) = 1.3465

f(0.6) = ln((

4(0.6))) + 2(0.6) = 1.6377

1

f(0.7) = ln((

4(0.7))) + 2(0.7) = 1.9148

f(0.8) = ln((

4(0.8))) + 2(0.8) = 2.1815

f(0.9) = ln((

4(0.9))) + 2(0.9) = 2.4404

f(1.0) = ln((

4(1.0))) + 2(1.0) = 2.6931

f(1.1) = ln((

4(1.1))) + 2(1.1) = 2.9408

f(1.2) = ln((

4(1.2))) + 2(1.2) = 3.1843

f(1.3) = ln((

4(1.3))) + 2(1.3) = 3.4243

f(1.4) = ln((

4(1.4))) + 2(1.4) = 3.6613

f(1.5) = ln((

4(1.5))) + 2(1.5) = 3.8958

f(1.6) = ln((

4(1.6))) + 2(1.6) = 4.1281

f(1.7) = ln((

4(1.7))) + 2(1.7) = 4.3584

f(1.8) = ln((

4(1.8))) + 2(1.8) = 4.587

f(1.9) = ln((

4(1.9))) + 2(1.9) = 4.814

4 Calculando f(x) * base:

0.258 0.1 = 0.02580.2884 0.1 = 0.028840.6911 0.1 = 0.069111.035 0.1 = 0.10351.3465 0.1 = 0.134651.6377 0.1 = 0.163771.9148 0.1 = 0.19148

2

2.1815 0.1 = 0.218152.4404 0.1 = 0.244042.6931 0.1 = 0.269312.9408 0.1 = 0.294083.1843 0.1 = 0.318433.4243 0.1 = 0.342433.6613 0.1 = 0.366133.8958 0.1 = 0.389584.1281 0.1 = 0.412814.3584 0.1 = 0.435844.587 0.1 = 0.45874.814 0.1 = 0.4814

X f(x) f(x) base0 0 0

0.1 0.258 0.02580.2 0.2884 0.028840.3 0.6911 0.069110.4 1.035 0.10350.5 1.3465 0.134650.6 1.6377 0.163770.7 1.9148 0.191480.8 2.1815 0.218150.9 2.4404 0.244041.0 2.6931 0.269311.1 2.9408 0.294081.2 3.1843 0.318431.3 3.4243 0.342431.4 3.6613 0.366131.5 3.8958 0.389581.6 4.1281 0.412811.7 4.3584 0.435841.8 4.587 0.45871.9 4.814 0.48142.0

(f(x) base) = 5.51844

3

20ln((

4x)) + 2xdx

= 20ln((

4x))dx + 20

2xdx

= (x ln((2x)) x2) + (x2)|20

= [2 ln((22)) 22

+ (22)] [0 ln((20)) 02

+ (02)]

= 5.07944 0

= 5.07944

4