Question

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method.

y = −x² + 11x − 30, y = 0; about the y−axis

Answer 1

To find the volume of the solid obtained by rotating the region bounded by the curves about the y-axis, we can use the disk method.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves about the y-axis, we can use the disk method. First, we need to find the limits of integration by setting the two curves equal to each other:

-x^2 + 11x - 30 = 0

Solving the equation, we get x = 3 and x = 10. So the limits of integration are from x = 3 to x = 10.

Now, we can calculate the volume using the formula V = ∫[a,b] π(y)^2 dx, where a = 3, b = 10, and y = -x^2 + 11x - 30.

Substituting the values and evaluating the integral, we get the volume of the solid obtained by rotating the region about the y-axis.