Question

Can someone help me with the steps needed to solve problems like this

Answer 1

i'm guessing take the integral first.. not sure what to do with the n=4

Answer 2

They want you to evaluate the integral using simpsons and trapezoid rule.

Answer 3

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

Answer 4

\[\small \int\limits_{a}^{b} f(x)dx \approx\frac{ \Delta x }{ 2 }\left[ f(x _{0})+2f(x _{1})+2f(x _{2})+2f(x _{3})+...+2f(x _{n-2})+2f(x _{n-1})+f(x _{n}) \right]\] and here is the trapezoid rule

Answer 5

Now you may approximate the integral