Calculus

Calculus of Parametric Equations

Parametric Equations - Surface Area

         

What is the surface area SS of the body of revolution obtained by rotating the curve y=ex,y=e^x, 0x1,0 \le x \le 1, about the xx-axis?

What is the surface area SS of the body of revolution obtained by rotating the parametric curve x=8t2+9y=4t0t1\begin{array}{c}&x = 8 t^2 + 9 &y = -4 t &0 \leq t \leq 1 \end{array} about the xx-axis?

What is the surface area SS of the solid of revolution obtained by rotating the parametric curve x=4ty=6t0t2\begin{array}{c}&x = 4 t &y = 6 t &0 \leq t \leq 2 \end{array} about the yy-axis?

What is the surface area SS of the body of revolution obtained by rotating the parametric curve x=7costy=7sint0tπ\begin{array}{c}&x = 7 \cos t &y = 7 \sin t &0 \leq t \leq \pi \end{array} about the xx-axis?

If SS is the surface area of the solid obtained by rotating the parametric curve x=4cos3ty=4sin3t0tπ2\begin{array}{c}&x = 4 \cos^3 t &y = 4 \sin^3 t &0 \leq t \leq \frac{\pi}{2} \end{array} about the xx-axis, what is 52S?\frac{5}{2}S?

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