2019 AP Calculus AB FRQ #3

The continuous function f is defined on the closed interval −6 to 5. The figure above shows a portion of the graph of f, consisting of two line segments and a quarter of a circle centered at the point (5, 3). It is known that the point (3, 3 − sqrt(5)) is on the graph of f. (a) If ∫ f(x) dx from -6 to 5 = 7, find the value of ∫ f(x) dx from -6 to -2. Show the work that leads to your answer. (b) Evaluate ∫ (2f’(x) + 4) dx from 3 to 5. (c) The function g is given by g(x) = ∫ f(t) dt from -2 to x. Find the absolute maximum value of g on the interval − 2 to 5. Justify your answer. (d) Find lim x→ infinity of 10^x − 3 * f’(x) / f(x)− arctan x . Timestamps Intro: 00:00 Part a: 00:22 Part b: 06:10 Part c: 08:21 Part d: 12:53