Final answer:
To find the volume of the solid generated by revolving the region bounded by y = cos x and y = 0 from x = 0 to a missing value, about the x-axis, you can use the method of cylindrical shells. Evaluate the integral of 2πx(cos x - 0) from x = 0 to the intersection point of y = cos x and y = 0 to find the volume of the solid.
Step-by-step explanation:
The question asks to find the volume of the solid generated by revolving the region bounded by y = cos x and y = 0 from x = 0 to a missing value, about the x-axis.
To find the volume, we can use the method of cylindrical shells. The volume of a cylindrical shell is given by 2πx(f(x)-g(x))dx, where f(x) is the upper function and g(x) is the lower function.
Since the region is bounded by y = cos x and y = 0, the upper function is f(x) = cos x and the lower function is g(x) = 0.
Now, we need to find the interval of integration, which is the x-value where y = cos x and y = 0 intersect. This occurs when cos x = 0, which gives us x = π/2.
Using the formula for the volume of a solid of revolution, the volume of the solid generated by revolving the region bounded by y = cos x and y = 0 from x = 0 to x = π/2 about the x-axis is given by:
V = 2π∫0π/2x(cos x - 0) dx
Simplifying the integral and evaluating it gives us the volume of the solid.