Questions from General Calculus

Q: The centroid of a curve can be found by a process similar

The centroid of a curve can be found by a process similar to the one we used for finding the centroid of a region. If C is a curve with length L, then the centroid is (x, y) where / Here we assign app...

Q: The Second Theorem of Pappus is in the same spirit as Pappus’s

The Second Theorem of Pappus is in the same spirit as Pappus’s Theorem on page 565, but for surface area rather than volume: Let C be a curve that lies entirely on one side of a line l in the plane. I...

Q: Use the Second Theorem of Pappus described in Exercise 48 to find

Use the Second Theorem of Pappus described in Exercise 48 to find the surface area of the torus in Example 7.

Q: Let 5 be the region that lies between the curves /

Let 5 be the region that lies between the curves where m and n are integers with 0 (a) Sketch the region /. (b) Find the coordinates of the centroid of /. (c) Try to find values of m and n such that t...

Q: Evaluate the integral using integration by parts with the indicated choices of

Evaluate the integral using integration by parts with the indicated choices of u and dv.

Q: (a) Set up an integral for the area of the

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x­ axis and (ii) the y­ axis. (b) Use the numerical integration capability of a ca...

Q: (a) Set up an integral for the area of the

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x axis and (ii) the y axis. (b) Use the numerical integration capability of a calculator to evaluate the...

Q: (a) Set up an integral for the area of the

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x axis and (ii) the y axis. (b) Use the numerical integration capability of a calculator to evaluate the...

Q: (a) Set up an integral for the area of the

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x axis and (ii) the y axis. (b) Use the numerical integration capability of a calculator to evaluate the...

Q: (a) Set up an integral for the area of the

(a) Set up an integral for the area of the surface obtained by rotating the curve about (i) the x axis and (ii) the y axis. (b) Use the numerical integration capability of a calculator to evaluate the...