# Speed Profile - Numerical Integration

• Hurly
In summary, the problem involves finding the total distance traveled for an object using a speed profile that is the absolute value of the velocity before integrating. The function to be numerically integrated using the Trapezium Rule is given, along with the necessary values of h, N, and total area. The goal is to calculate the total area under the curve for a data set by starting with an h value of 0.1 and decreasing it until the last two calculations are within 0.0005 of each other or h becomes 0.00001. The velocity and speed profiles are defined by three coefficients and the interesting thing about the velocity profile is that it is undefined at x = 0. The necessary equations and attempt at a solution

## Homework Statement

I need to find total distance traveled for an object using the speed profile

which is the absolute value of velocity before integrating. so we finish up with the total distance travelled, rather than the final displacement from the initial position.

And this is the function i need to numerically integrate using the The Trapezium Rule.
Needed Values:

The h Value-
The N Value-
The Total Area-

I Have Data Sets Which is Shown In The Picture Below

http://imageshack.us/f/69/numericalintegration.png/

NOTE:
Calculate the total area under the curve for a data set, starting with an h value of 0.1 and then continuing with h = 0.01, 0.001, etc. until the latest two calculations are within 0.0005of each other, or h becomes 0.00001.

Could Someone Use One of The Data Sets to Show Hows it Done Then i'll Do The Rest of Them

## Homework Equations

Velocity Profile V(x) = x2+ b. x1+c x0+ d.x-1

defined by the 3 coefficients for the powers of x1, x0, and x-1:
Remember that
x1 = x
x0 = 1
x-1 = $\frac{1}{x}$

So, the most interesting thing about this velocity profile is that it is undefined when x equals 0.

Speed Profile Sp(x) = |x2+ b. x1+c x0+ d.x-1|

Areai = h $\frac{F(xi)+F(xi+1)}{2}$

with Xi+1 = x1+h

N = $\frac{(xfinal-xinitial)}{h}$

Total Area = Sum of the Areai values from 0 to N-1

## The Attempt at a Solution

|x2+ b. x1+c x0+ d.x-1|
|x2+ 1. x1+4 x0+ -6.x-1|

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Can Anyone Help me or Point me in the right direction>?