Question

a rectangle is bounded by the x-axis and the semicircle y=radical 36-x^2. write the area A of the rectangle as a function of x, and determine the domain of the function

Answer 1

The area between a function, and the x-axis is given by the integral of the function with respect to x, with limits where you choose them (in this case, you'll want to pick limits where y=0:
\(y=f(x)\)
\[Area = \int_a^b f(x)dx\]