Question

Simpson's Rule ?

Answer 1

8. Using the Simpson's Rule (with six subintervals), write and evaluate an expression to approximate the value of \[A(90)=\int\limits_{0}^{90}R(t)dt\]Indicate the units of your answer.

Answer 2

t 0 15 30 45 60 75 90
R(t) 20 35 63 78 73 60 56

Answer 3

the units are probably gallons/min

Answer 4

\[\int\limits_{a}^{b} f(x)dx \approx S _{n} = \frac{ \Delta x }{ 3 }\left[ f(x _{0})+4f(x _{1})+2f(x _{2})+4f(x _{3})+...+2f(x _{n-2})+4f(x _{n-1})+f(x _{n}) \right]\]

Answer 5

\[S _{n} = \frac{ \Delta x }{ 3 }\left[ f(x _{0})+4f(x _{1})+2f(x _{2})+4f(x _{3})+...+2f(x _{n-2})+4f(x _{n-1})+f(x _{n}) \right]\]

Answer 6

Where n is even and \[\Delta x =(b-a)/n\]