Questions from General Calculus

Q: Use a CAS to find the exact area of the surface obtained

Use a CAS to find the exact area of the surface obtained by rotating the curve about the y axis. If your CAS has trouble evaluating the integral, express the surface area as an integral in the other v...

Q: If the infinite curve y = ex, x > 0,

If the infinite curve y = ex, x > 0, is rotated about the x­ axis, find the area of the resulting surface.

Q: (a) If a > 0, find the area of

(a) If a > 0, find the area of the surface generated by rotating the loop of the curve 3ay2 = x (a - x)2 about the x­ axis. (b) Find the surface area if the loop is rotated about the y­ axis.

Q: A group of engineers is building a parabolic satellite dish whose shape

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax2 about the y­ axis. If the dish is to have a 10­ft diameter and a maximum depth of 2...

Q: Find the surface area of the torus in Exercise 6.2

Find the surface area of the torus in Exercise 6.2.63. Data from Exercise 6.2.63: (a) Set up an integral for the volume of a solid torus (the donut-shaped solid shown in the figure) with radii r and...

Q: If the curve y = f(x), a < x

If the curve y = f(x), a < x < b, is rotated about the horizontal line y = c, where f(x) < c, find a formula for the area of the resulting surface.

Q: Use the result of Exercise 33 to set up an integral to

Use the result of Exercise 33 to set up an integral to find the area of the surface generated by rotating the curve / 0 < x < 4, about the line y = 4. Then use a CAS to evaluate the integral. Data fr...

Q: Find the area of the surface obtained by rotating the circle x2

Find the area of the surface obtained by rotating the circle x2 + y2 = r2 about the line y = r.

Q: Show that if we rotate the curve y = ex/2

Show that if we rotate the curve y = ex/2 + ex/2 about the x­ axis, the area of the resulting surface is the same value as the enclosed volume for any interval a < x < b.

Q: Let L be the length of the curve y = f(

Let L be the length of the curve y = f(x), a < x < b, where f is positive and has a continuous derivative. Let Sf be the surface area generated by rotating the curve about the x­ axis. If c is a posit...