Question

Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson's Rule to approximate the integral 0∫3((1)/(1+y^5))dy with n=6. Give each answer correct to six decimal places.

Answer 1

so create a table using f(y) = 3/(1+y^5)

y : 0 : 0.5 : 1 : 1.5 : 2 : 2.5 : 3:
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f(y) : 3 : 2.90 : 1.5 : 0.35: 0.09 : 0.03 : 0.01


I'd use repeated applications of the trapezoidal rule

\[A= \frac{h}{2}(f(y_{n}) + f(y_{n +1})\]

which when added can be written as

A = 0.5/2[(f(0) + f(3) + 2(f(0.5) + f(1) + f(1.5) + f(2) + f(2.5))]

just make the necessary substitutions and evaluate.

Hope it helps

Answer 2

so it should be (1/4)(3+.01+2(2.9)+1.5+.09+.03)?

Answer 3

so thats the trapezoid approximation,

Answer 4

oops 0.5 divide by 2 is 0.25

Answer 5

so I was correct the first time?

Answer 6

If your 1st attempt is the one shown above, then yes...

Answer 7

i GOT it, thanks