Question

A rectangle is bound by the x-axis and the semicircle `y=(36-x^2)^(1/2)`. Write the area of the rectangle as a function of x?

Answer 1

`S_("rectangle")=|x|*(36-x^2)^(1/2)` for `"x in [-6, 6]`

Explanation:

`S_("rectangle")=base*height`
`base=x` if `x>=0` and `base =-x` if `x<0` => `base =|x|`
`height=y`
`S_("rectangle")=|x|*y` => `S_("rectangle")=|x|.(36-x^2)^(1/2)`
This area is only defined for x in the interval from -6 to 6.