I need help with B) cos(ax) 1. Given the integral dr. Answer the following (a) (

Question

I need help with B)

cos(ax) 1. Given the integral dr. Answer the following (a) (4pt) If the interval of integration is divided into 6 subintervals of equal width, determine the exact values of f(xof), f(r2) f(rs),f(6) (b) (4pt) Use the values in part a to estimate the value of the integral using the Trapezoidal Rule with n 6. (c) (4pt) Use the values in part a to estimate the value ofthe integral using Simpson's Rule with n 6. (d) (4pt) If you wanted to guarantee that the error of the estimation using Simpson's Rule is less than 0.003 units, how many subdivisions should you use? (Note: Using appropriate technology, the absolute maximum of f()on the interval is 47.951.)

Explanation / Answer

B)

f(x)=(cos(x))/x

a=1 ,b=3 ,n=6,x=[3-1]/6 =(1/3)

xo=1,x1=(4/3),x2=(5/3),x3=2,x4=(7/3),x5=(8/3),x6=3,

f(xo)=(cos(*1))/1 =-1,f(x1)=(cos(*4/3))/(4/3)=(-3/8),f(x2)=(cos(*5/3))/(5/3)=(3/10),f(x3)=(cos(*2))/(2)=(1/2),

f(x4)=(cos(*7/3))/(7/3)=(3/14),f(x5)=(cos(*8/3))/(8/3)=(-3/16),f(x6)=(cos(*3))/(3)=(-1/3)

trapezoidal rule:

T6 =(x/2)*[f(xo)+2*f(x1)+2*f(x2)+2*f(x3)+2*f(x4)+2*f(x5)+f(x6)]

T6 =(1/6)*[(-1)+2*(-3/8)+2*(3/10)+2*(1/2)+2*(3/14)+2*(-3/16)+(-1/3)]

T6 = -361/5040 exactly

T6 = -0.071627 approximately

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