(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!

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 $\sqrt[4]{5}$ instead of 0: the correct value is 3.162682.

- Hollywood

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