Trapezoidal, Midpoint, and Simpson's question. please help!

http://www.webassign.net/cgi-perl/sy...n%20%3D%208%20

(a) Use the Trapezoidal Rule to approximate the given integral with the specified value of *n*. (Round your answer to six decimal places.)

(b) Use the Midpoint Rule to approximate the given integral with the specified value of *n*. (Round your answer to six decimal places.)

(c) Use Simpson's Rule to approximate the given integral with the specified value of *n*. (Round your answer to six decimal places.)

I got a) 2.789267

b)1.581091

c)3.038070

my work:

a) T8= (1/8)*[ fourthroot(5+(1/4)^{2})+2*fourthroot(5+(1/2)^{2})+2*fourthroot(5+(3/4)^{2})+2*fourthroot(5+1)+2*fourthroot(5+(5/4)^{2})+2*fourthroot(5+(6/4)^{2})+2*fourthroot(5+(7/4)^{2})+fourthroot(9) ]

b)M8= (1/8)*[ fourthroot(5+(1/8)^2) +fourthroot(5+(3/8)^2)+fourthroot(5+(5/8)^2)+fourthroot(5+(7/8)^2)+fourthroot(5+(9/8)^2)+fourthroot(5+(11/8)^2)+fourthroot(5+(13/8)^2)+fourthroot(5+(15/8)^2) ]

c) S8=(1/12)*[ 0+ 4*fourthroot(5+(1/4)^{2})+2*fourthroot(5+(1/2)^{2})+4*fourthroot(5+(3/4)^{2})+2*fourthroot(5+1)+4*fourthroot(5+(5/4)^{2})+2*fourthroot(5+(6/4)^{2})+4*fourthroot(5+(7/4)^{2})+fourthroot(9) ]

Any help greatly greatly appreciated; this problem is driving me crazy.

Thanks!

Re: Trapezoidal, Midpoint, and Simpson's question. please help!

For the trapezoidal rule, you started at 1/4 instead of 0: the correct value is 3.163686.

For the midpoint rule, you just multiply by the length of the interval, 1/4: the correct value is twice what you have, 3.162182.

For Simpson's rule, you should have $\displaystyle \sqrt[4]{5}$ instead of 0: the correct value is 3.162682.

- Hollywood

Re: Trapezoidal, Midpoint, and Simpson's question. please help!

Thank you so much!! Thanks for the explanation of my errors as well!!!