Question

Estimate the surface area of the oil spill using the Trapezoidal Rule.

Answer 1

\[\int\limits_{a}^{b} f(x)dx \approx\frac{ \Delta x }{ 2 }\left[ f(x _{0})+2f(x _{1})+2f(x _{2})+2f(x _{3})+...+2f(x _{n-2})+2f(x _{n-1})+f(x _{n}) \right]\] here is the trapezoidal rule, where delta x is \[\Delta x = \frac{ b-a }{ n }:~~~x_i = a+i \Delta x\]

Answer 2

So try it out and see what you get :)

Answer 3

I am a bit unsure where to start. I have done the trapezoidal rule when there is a graph, but I am confused on this.

Answer 4

Use your image as you would a graph

Answer 5

So start off by finding delta x

Answer 6

Would delta x be 4?

Answer 7

Yeah, that looks good

Answer 8

I am having a really hard time with this, could you please show me how to do it? I can get what I need if I know what delta x is and what number corresponds to x0, x1, x2 etc. I just don't know how to do this since it is not formatted in the way that I am used to.

Answer 9

So I attempted this and got 1919.8 miles as the surface area. Is this correct?

Answer 10

Hey, do you still need help?