Math and science students use graphing calculators to plot two-dimensional graphs of functions, solve equations, and calculate derivatives and integrals. In calculus, you can find the arc length of a curve by evaluating an integral related to the curve's equation. A graphing calculator can evaluate the integral in less than a second, whereas by hand it may take several minutes depending on the complexity of the function.
Instructions
1. Write down the derivative of the function whose arc length you want to compute. For example, suppose you are calculating the arc length of f(x) = e^(2x) over a finite interval. The derivative of this function is f ' (x) = 2e^(2x).
2. Open the integral evaluation screen on your graphing calculator. On Texas Instruments devices, do this by hitting the "MATH" button, choosing the "Math" menu and then selecting "fnInt" from the drop down submenu.
3. Enter the function sqrt(1 + (f ' (x))^2) on the screen and enter a comma at the end of the function. Replace "f ' (x)" with the derivative of the function you are working on. The expression sqrt(1 + (f ' (x))^2) is the formula for the arc length of a function f(x). For instance, if f(x) = e^(2x) and f ' (x) = 2e^(2x) then you enter sqrt(1 + (2e^(2x))^2) followed by a comma.
4. Enter "x" followed by a comma. You must do this so the calculator knows what the variable is.
5. Enter the lower endpoint of the arc's interval, followed by a comma. For instance, if you are evaluating the arc length over the interval from 3 to 4, you enter 3 followed by a comma.
6. Enter the upper endpoint of arc's interval followed by a closing parenthesis. For instance, if 4 is the upper endpoint, you enter 4).
7. Hit the enter key to evaluate the integral. The length of the arc will appear below the commands you entered.
No comments:
Post a Comment