What is the surface area produced by rotating #f(x)=cscxcotx, x in [pi/8,pi/4]# around the x-axis?
1 Answer
Apr 11, 2018
To find the surface area of the figure, we need to integrate the circumference of the figure with respect to
Since we're rotating around the x-axis, the radius of the circle is
#int_(pi/8)^(pi/4)(2pir) dx#
#2piint_(pi/8)^(pi/4) cscxcotxdx#
#2pi (-cscx)]_(pi/8)^(pi/4)#
#-2pi(csc(pi/4)-csc(pi/8))#
#-2pi(sqrt(2) - sqrt(2/(1-cos(pi/4))))" "" "# (using half-angle formula)
#-2pi(sqrt(2) - sqrt(2/(1-sqrt2/2)))#
#-2pi(sqrt(2) - 2/sqrt(2-sqrt2))#
This is the final value, which can be simplified in various ways, as necessary. As a decimal, it is
Therefore, the surface area of the shape produced by rotating the function
Final Answer