The area of the upper half of the circle whose equation is (x-1)^2+y^2=1 is given by

Step-by-step solution

The given equation of the circle is (x-1)^2 + y^2 = 1 . Expanding the equation, we get x^2 - 2x + 1 + y^2 = 1 , which simplifies to x^2 + y^2 - 2x = 0 . Solving for y , we have y^2 = 2x - x^2 , which gives y = 2x - x^2 . The upper half of the circle corresponds to y = 2x - x^2 . The circle (x-1)^2 + y^2 = 1 has its center at (1, 0) and radius r = 1 . Thus, the circle extends from x = 1 - 1 = 0 to x = 1 + 1 = 2 . The area of the upper half is given by the integral of y with respect to x from the leftmost point to th