Question

Πr(x) = {(3/4)[1 - (8 - r)²] for 7 ≤ r ≤ 9=0 otherwise}

What is the expected area of the resulting circular region?

Answer 1

The expected area of the resulting circular region can be calculated by taking the integral of the area function πr(x) over the range of r values for which it is defined. To find the expected area, evaluate the integral of the area function from the lower limit to the upper limit of the range.

Step-by-step explanation:

The expected area of the resulting circular region can be calculated by taking the integral of the area function πr(x) over the range of r values for which it is defined. In this case, the function is defined as {(3/4)[1 - (8 - r)²] for 7 ≤ r ≤ 9=0 otherwise}. So, the expected area is given by:

Expected Area = ∫[(3/4)[1 - (8 - r)²]] dr from 7 to 9

To evaluate this integral, you can use integral techniques such as substitution or integration by parts. Once you find the antiderivative of the integrand, you can evaluate it at the upper and lower limits of integration to find the expected area.