Question

Calc question,help please?

Answer 1

I don't recall the trapezoid rule off the top of my head, but here's a tip. Since they gave you the width each spot, use that as your \[\Delta x\] and then set f(x) equal to each of those vertical points. does that make sense?

Answer 2

For example, try putting the spill in a coordinate plane and where f(x)=11 let x = 4.

Answer 3

And the next vertical line be f(8)=13.5

Answer 4

In real life, you seldom get pretty equations to play with. Instead you'll typically be estimating area a couple known point like this. :)

Answer 5

Trapezoid rule is just a sum of the trapezoid formula: \[\sum_{n=1}^{\infty}\frac{h}{2}(b_{n-1}+b_n) = \frac{h}{2}(b_1+b_2)+\frac{h}{2}(b_2+b_3)+...+\frac{h}{2}(b_{n-1}+b_n)\]In this equation h will be a constant (the distance between bases, so in this case 4 miles). And then we can simplify the equation by using some algebraic manipulation. Since h/2 is a constant, we can factor it out giving:\[\frac{h}{2}((b_1+b_2)+(b_2+b_3)+...+(b_{n-1}+b_n))\] Now notice that we will see every base twice, except for b(1) and b(n), thus we can simplify it further to \[\frac{h}{2}((b_1+2(b_2+b_2+b_3+...+b_{n-1})+b_n))\] And that would be your trapezoid rule.

As for Simpsons Rule I only remember it (vaguely) in terms of Calc 2, which probably would just be confusing for you. sorry :/

Answer 6

@lxry0h