Question

Let f : [0, ∞) → R be a continuous function such that

for all x ∈[0, ∞). Then, which of the following statement(s) is (are) TRUE ? 

(A) The curve y = f(x) passes through the point (1, 2) 

(B) The curve y = f(x) passes through the point (2, -1)

(C) The area of the region {(x, y) ∈ [0, 1] x R : f(x) ≤  y ≤ √(1 - x²)} is (π -2)/4

(D) The area of the region {(x, y) ∈ [0, 1] x R : f(x) ≤  y ≤ √(1 - x²)} is (π -1)/4

Answer 1

solution B,C

put x = 0, f(0) = 1 => C = 0