Many integrals (such as
e-x2dx and
dt) cannot be evaluated exactly, but you get numerical
approximations by choosing Evaluate Numerically.
Evaluate Numerically
e-x2dx = .7468241328 6pt
dt = 1.851937052
Integrals associated with arc lengths of curves can almost never be evaluated exactly.
Given a curve y = f (x), the arc length between x = a and x = b is given by the integral
For example, given f (x) = x sin x, consequently, f′(x) = sin x + x cos x, you can find the length of the arc between x = 0 and x = π by applying Evaluate Numerically.
Evaluate Numerically
dx =
dx = 5.04040692
Curves in the plane or three-dimensional space can also be represented parametrically.
The preceding example can be visualized graphically. In the Plot Properties tabbed dialog, set the Plot Style to Hidden Line, the Sample Size to 99, the Radius to 1/8, and the Domain Interval to 0≤t≤16π = 50.265; choose Equal Scaling on Each Axis.
Plot 3D + Tube
cos t,
sin t,
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dtbpF3in2.0003in0pt