Compute the integral
\int -x^(2)csc^(2)(x^(3)+1)dx
Find the area of the region bounded by the curves
y=\sqrt(x+1),y=(1)/(x+1)
and
x=4
. Consider the region bounded by
y=(1)/(4)x^(2)
and
y=(1)/(2)x
(a) Use cylindrical shells to find the volume of the solid generated by rotating the above region about the y-axis. (b) Use Washer method to find the volume of the solid generated by rotating the above region about the
x_()
-axis. Determine if the following are a type 1 or type 2 improper integral. If the integral converges find the value, otherwise say it diverges. (a)
\int_3^(\infty ) (1)/((x-2)^((3)/(2)))dx
(b)
\int_0^5 (1)/(\root(3)(5-x))dx