Suppose that f is a function which is integrable on the entire real line, and that a and b are real numbers. Which of the following statements are true? Check each one that is true. ✔f f(x) dx = f f(t) dt ✓fa f(x) dx = 0 □ ſå f(x) dx = f(x) dx få f(x) dx = x₂ = a +iAx. f(x1)Ax+ƒ(x2)^x + ··· + f(xn)Aï where n is a positive integer, Ax = (b-a)/n and for each i we define Ofan dx = (b-a)/n for any real number n Of f(x) dx ≥ 0 because it always measures the area of a region. ✔fa f(x) dx = f f(x) dx - f f(x) dx for any real number c. ✔ If f(x) ≤ g(x) for all x then f f(x) dx ≤ f g(x) dx.

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