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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

Sagot :

ajdonis

Answer:

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:

[tex]V=2\pi\int\limits^a_b {rh} \, dr[/tex]

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 [tex]x=\pi[/tex]. So the volume is found by using the following integral:

[tex]V=2\pi\int\limits^\pi_0 {xsin x} \, dx [/tex]

View image ajdonis
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