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Example 1We begin by computing arc-length of our helix from To compute arc-length we want to sum the lengths dl of each of our infinitesimal
pieces of P. Since we are integrating dl which is Tdl where T
is the unit vector in the direction tangent to P, which is the direction of The integrand here is then the absolute value of Example 2Compute the work done by the force of gravity when the naughty child throws
a stone of mass M out the window and it lands on the ground 30 feet below the
window. The work done here is given by the line integral over the path of the
stone of F in appropriate units no matter what the path was. |
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