Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) 5 3 cos(4x) x dx, n

1.1061427

Correct Value (Using calculator) = 0.927007

Step-by-step explanation:

b=5, a=1, n=8,

h=(b-a)/n=(5-1)/8=0.5

f(x) = 5*cos(4x)/x

The sub-intervals are,

[1, 1.5], [1.5, 2], [2, 2.5], [2.5, 3], [3, 3.5], [3.5, 4], [4, 4.5], [4.5, 5]

Let the integral be denoted by I.

a) From Trapezoidal Rule:

I = [h/2] { f(x0) + 2f(x1) + 2f(x2) + 2f(x3) + 2f(x4) + 2f(x5) + 2(x6) + 2f(x7) + f(x8) }

= [0.5 / 2] { f(1) + 2f(1.5) + 2f(2) + 2f(2.5) + 2f(3) + 2f(3.5) + 2f(4) + 2f(4.5) + f(5) }

= [0.25] { -3.2682 + 2*3.2005 + 2*-0.36375 + 2*-1.6781 + 2*1.4064 + 2*0.19533 + 2*-1.1970 + 2*0.7336 + 0.40808}

= 0.433489

b) From Midpoint Rule:

Values are calculated at midpoint of each interval

I = [h] { f(x1*) + f(x2*) + f(x3*) + f(x4*) + f(x5*) + (x6*) + f(x7*) + f(x8*) }

= [0.5] { f(1.25) + f(1.75) + f(2.25) + f(2.75) + f(3.25) + f(3.75) + f(4.25) + f(4.75) }

= 1.186071

c) Simpson's Rule:

I = [h/3] { f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + 2f(x4) + 4f(x5) + 2(x6) + 4f(x7) + f(x8) }

= [0.5 / 3] { f(1) + 4f(1.5) + 2f(2) + 4f(2.5) + 2f(3) + 4f(3.5) + 2f(4) + 4f(4.5) + f(5) }

= [0.25] { -3.2682 + 4*3.2005 + 2*-0.36375 + 4*-1.6781 + 2*1.4064 + 4*0.19533 + 2*-1.1970 + 4*0.7336 + 0.40808}

= 1.1061427

Correct Value (Using calculator) = 0.927007

the answer would be the last one (constat) she stays at the same rat every two mintues it goes up by 0.4

step-by-step explanation:

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841