Calculus of Parametric Equations
What is the surface area \(S\) of the body of revolution obtained by rotating the curve \(y=e^x,\) \(0 \le x \le 1,\) about the \(x-\)axis?
What is the surface area \(S\) of the body of revolution obtained by rotating the parametric curve \[\begin{array} &x = 8 t^2 + 9 &y = -4 t &0 \leq t \leq 1 \end{array}\] about the \(x\)-axis?
What is the surface area \(S\) of the solid of revolution obtained by rotating the parametric curve \[\begin{array} &x = 4 t &y = 6 t &0 \leq t \leq 2 \end{array}\] about the \(y\)-axis?
What is the surface area \(S\) of the body of revolution obtained by rotating the parametric curve \[\begin{array} &x = 7 \cos t &y = 7 \sin t &0 \leq t \leq \pi \end{array}\] about the \(x\)-axis?
If \(S\) is the surface area of the solid obtained by rotating the parametric curve \[\begin{array} &x = 4 \cos^3 t &y = 4 \sin^3 t &0 \leq t \leq \frac{\pi}{2} \end{array}\] about the \(x\)-axis, what is \(\frac{5}{2}S?\)