The formula for finding the length of a curve is given by the integral of the square root of the sum of the squares of the derivatives of the curve with respect to the independent variable. In this case, the formula would be ∫√(1+(3t)^2+(8t^(3/2))^2+(12t^2)^2)dt.
To solve for the length of a curve, you need to first find the integral of the square root of the sum of the squares of the derivatives of the curve. Then, you can plug in the limits of integration (usually the starting and ending points of the curve) and evaluate the integral using calculus techniques such as u-substitution or integration by parts.
Yes, you can use a calculator to find the length of a curve. However, you will need to use a graphing calculator or a computer program with a built-in integration function. Simply input the equation for the curve and the limits of integration, and the calculator will give you the numerical value for the length.
The unit for measuring the length of a curve will depend on the units used for the independent variable in the equation. In this case, if t is measured in seconds, then the length of the curve would be measured in seconds. You can also use unit conversions to change the units to a more appropriate form, such as meters or centimeters.
Unfortunately, there is no shortcut for finding the length of a curve. You will need to use the formula and perform the necessary calculations to find the length. However, using a calculator or computer program can make the process easier and faster.