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Answer:
f(x) = (π-2)x^2/4
Step-by-step explanation:
The area of the triangle is ...
A = 1/2(x)(x) = (1/2)x^2
The hypotenuse of the triangle is x√2, so the radius of the circle is x/√2. That means the area of the semicircle is ...
A = 1/2πr^2 = (π/2)(x/√2)^2 = (π/4)x^2
The shaded area is the difference between the semicircle area and the triangle area.
f(x) = (π/4)x^2 -(1/2)x^2
f(x) = (π-2)x^2/4
