Find the surface area generated by rotating a given parametric curve about the x-axis using a Computer Algebra System.

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Surface Area of a Parametric Curve Using a CAS

Parametric equations and vector functions core

[T] Use a CAS to find the area of the surface generated by rotating \(x = t + t^3, y = t - \frac{1}{t^2}, 1 \le t \le 2\) about the x-axis. (Answer to three decimal places.)

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What you need first

the formula for the surface area of revolution for parametric curves
the power rule for derivatives
how to use a Computer Algebra System (CAS) for numerical integration

What this problem tests

Tests the ability to correctly set up a surface area integral for a parametric curve and use technology to evaluate it.

This problem typically appears in a Calculus II or Multivariable Calculus course when discussing applications of parametric equations.

Surface Area of a Parametric Curve Using a CAS

What you need first

What this problem tests

More on Parametric equations and vector functions