Final answer:
To find the volume of the glass formed by rotating the shaded region about the y-axis, we can use the formula V = Ah, where A is the cross-sectional area and h is the height of the glass.
Step-by-step explanation:
To find the volume of the glass formed by rotating the shaded region about the y-axis, we can use the formula V = A*h, where A is the cross-sectional area and h is the height of the glass. In this case, the cross-sectional area is given by the integral of the function y = x^4/2, which represents the curve that forms the inside of the glass.
To find the limits of integration, we need to determine the x-coordinates where the curve intersects the x-axis. Setting y = 0, we get x^4/2 = 0, which implies x = 0.
Thus, the volume of the glass can be calculated as follows:
V = ∫[0, b] (π*x^4/2) dx, where b is the x-coordinate where the curve intersects the x-axis.
We need to find the value of b. Setting y = 0, we get b^4/2 = 0, which implies b = 0.
Therefore, the volume of the glass is V = ∫[0, 0] (π*x^4/2) dx = 0.
The complete question is: A glass is formed by rotating the shaded region shown above about the y axis. The curve that forms the inside of the glass is the graph of y = x4/2. Length units in the figure are cm. What is the volume of the glass? (That is, what is the volume of the solid formed when the shaded region is rotated about the y axis?)