Question

find the volume obtained when shaded region is rotated through 360 about the x-axis

Answer 1

the area of a circle is pi r^2

the sum of the areas of the circles relates to the integration of the areas\[\int pi~r^2\]
\[\pi \int ~r^2\]
since the radius is defined by f(x)
\[\pi \int_{a}^{b} ~(f(x))^2~dx\]

Answer 2

Should i replace x = secx..?

Answer 3

the radius is defined by f(x) = sec(x) yes

so integrating r^2 = sec^2(x) is appropriate

Answer 4

thx buddy.. :)

Answer 5

youre welcome