\"Develop a program to numerically compute the integral of the function f(x)=sin

Question

"Develop a program to numerically compute the integral of the function f(x)=sin(x)/x
between two limits read from an input file.

The code should provide the results of the integrations using the 3 methods we have
learned (midpoint, trapezoidal and Simpson’s).

The code should provide an estimation of the error for each method.

Your code should avoid division by zero if necessary."


Working on this problem right now, but seem to even get close. I'll give full karma points to anyone who can write a program that does this for me with comments explaining what each line/section of the code does.

Thanks!

Explanation / Answer

Here ya are: ********************************** Program inttr double precision isum,x,xa,xb,h,f,I,a,IA,error,e integer j,p,k1,k2,k3,n,l dimension x(3),xa(3),xb(3),h(3),a(3) n=3 p=300 do j=1,n a(j)=rand() xa(j)=0 xb(j)=1 h(j)=(xb(j)-xa(j))/p enddo isum=0 error=0 c we have to use n do's one inside the other. In this case, n=3. c to calculate the error we need to compute the second partial c derivate of F do k1=1,p x(1)=xa(1)+(k1-1/2)*h(1) do k2=1,p x(2)=xa(2)+(k2-1/2)*h(2) do k3=1,p x(3)=xa(3)+(k3-1/2)*h(3) call func(a,x,f,n) isum=isum+f do l=1,n error=error+f*(a(l)**2) enddo enddo enddo enddo I=isum*(h(1)*h(2)*h(3)) e=(p**(-2/n))*error/(24*isum) IA=1 do j=1,n IA=IA*((exp(a(j))-1)/a(j)) enddo write(*,*) I,e,IA stop end SUBROUTINE func(a,x,f,n) double precision a,x,f,ax integer n,j dimension a(n),x(n) ax=0 do j=1,n ax=ax+a(j)*x(j) enddo f=exp(ax) end

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