Homework SourseUse Simpsons Rule with n10 to approximate the area of the su
Use Simpson\'s Rule with n=10 to approximate the area of the surface obtained by rotating the curve
y=x+sqrt(x), 1 less than or equal to x less than or equal to 2, about the x-axis.
Include at least five decimal places in your answer.
Area =
( I got 3.31046, but I\'m not sure if it\'s right)
thank you.
y=x+sqrt(x), 1 less than or equal to x less than or equal to 2, about the x-axis.
Include at least five decimal places in your answer.
Area =
( I got 3.31046, but I\'m not sure if it\'s right)
thank you.
Solution
h=(2-1)/10=0.1 the break points are 1,1.1,1.2,....,2 so area of surface=(h/3)*(f(1)+4*f(1.1)+2*f(1.2)+....+4*f(1.9)+f(2))=103.33896*0.1/3=3.44463 -------------------------------------------------------------------------------------- Matlab code for finding the sum :- x=[1:0.1:2]; format long; y=x+sqrt(x); sum=0; for i= 1:11 if(i==1 || i==11) sum=sum+y(i); else if i%2==0 sum=sum+4*y(i); else sum=sum+2*y(i); end end end sum
