Let `f:[0,oo)rarrR` be a continuous function such that `f(x)=1-2x+overset(x)underset(0)inte^(x-t)f(t)dt" for all "x in [0, oo).` Then, which of the following statements(s) is (are)) TRUE?

Options

A. The curve y = f (x) passes through the point (1, 2)
B. The curve y = f(x) passes throgh the point (2, –1)
C. The area of the region `{(x,y) in[0,1]xR:f(x)le y le sqrt(1-x^2)}` is `pi-2/4`
D. The area of the region `{(x,y) in [0,1]xR:f(X) ley le sqrt(1-x^2)}` is `pi-1/4`

Answer

B, C