Question

A rectangle is bounded by the x-axis and the semicircle y=sqrt(36-x^2) write the area a of the rectangle as a function of x

Answer 1

we are given

A rectangle is bounded by the x-axis and the semicircle y=sqrt(36-x^2)

we can see that

length=L=2x

width=W=y

we know that

area of rectangle is length*width

$A=L*W$

now, we can plug values

$A=2x*y$

$A=2x\sqrt{36-x^2}$..............Answer