A rectangle is bounded by the x-axis and the semicircle y = √(36 – x^2). Write the area A of the rectangle as a function of x, and determine the domain of the area function.

Question

anonymous · Answer

How can a rectangle be bounded by a straight line and a semicircle? I'm confused.

anonymous · Answer

this is the image of the problem

anonymous · Answer

hope this helps

anonymous · Answer

oh ok.

anonymous · Answer

Let (x,y) be the point on the diagram. Then the length of the rectangle is 2x and its breadth is y = sqrt(36-x^2). Thus its area f(x) is
$$f(x)=2x\sqrt{36-x^2}$$
Its domain would be $$x\in (-6,6)$$, as otherwise the rectangle wouldn't be defined.

anonymous · Answer

Sorry its domain would be $$x \in (0,6)$$ not as I stated previously.

anonymous · Answer

thank you