Final answer:
To find the volume of the solid of revolution formed by revolving the region bounded above by y=10/x², we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid of revolution formed by revolving the region bounded above by y=10/x², we can use the method of cylindrical shells.
First, let's find the limits of integration. Since the region is bounded above by y=10/x², we need to find the x-values where y=10/x² intersects the x-axis. Setting y=0, we get 10/x²=0, which means that x²=10. Taking the square root of both sides, we get x=±√10. However, since we are only considering the portion of the region where y>0, we only need to consider the positive square root, x=√10.
Next, let's find the equation of the curve that generates the solid of revolution. We have y=10/x², so we can rewrite it as x=√10/y^(1/2).
The volume of the solid of revolution can be calculated using the formula V=∫[a,b]2πx(f(x)-g(x))dx, where f(x) is the upper function and g(x) is the lower function. In this case, f(x) is √10/y^(1/2) and g(x) is 0. Plugging these values into the formula, we get V=∫[0,10]2π√10/y^(1/2)dy. Now we need to evaluate this integral to find the volume.