Sketch a plane region and indicate the axis about which it is revolved so that the resulting solid of revoltuion (found using the shell method) is given by the integral. π
2π∫ xsinx dx
0

See attached picture.

Step-by-step explanation:

The idea of the shell method is to find the volume of a differential shell by using the formula:

in the drawing we can see that r=x, h=sin x and dr=dx. The area is revolving about the y-axis from x=0 to . So the volume is found by using the following integral:

x

step-by-step explanation:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl