Question

How do I calculate the integral from 0 to 3 of (sqrt(9-x^2)+2) using high-school geometry?

Answer 1

Are you sure that you can calculate it using high school geometry?

Answer 2

Yeah, it is one of the questions on an old midterm

Answer 3

Here the answer key's answer, but it makes no sense to me

Answer 4

if you set y = sqrt(9-x^2)+2
then
y-2 = sqrt(9-x^2)
square both sides
(y-2)^2 = 9-x^2
x^2 + (y-2)^2 = 9
this is an equation of a circle centered at (0,2) with radius 3

Answer 5

now the graph in the picture is only this part