Question

Y=x(sin(x)), 0 ≤ x ≤ 2π?

Use Simpson s Rule with
n = 10
to estimate the arc length of the curve. Compare your answer with the value of the integral produced by your calculator. (Round your answers to six decimal places.)

*can you also tell me how u put it into the calculator to get an approximation? i have a ti inspire and my calculations have been wrong every time I've tried.

Answer 1

y'=(x)cos(x)+(sin(x))
(dy/dx)^2= x^2(cos(x))^2+(sin(x))^2?

Answer 2

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

Answer 3

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

Answer 4

yes but i have to do a calculator approximation as well
with the integral. i need to know what the correct integral would be for the problem when trying to find the arc length of a curve

Answer 5

Can you set it up?

Answer 6

\[\Delta x = \frac{ b-a }{ n }\]

Answer 7

Setting it up is more important than the answer