Let (x) = e 0.05x (1 + sin x). (a) Obtain a plot of (x) for 0 x 20, and discuss the behavior

Let ƒ(x) = e^−0.05x(1 + sin x).
(a) Obtain a plot of ƒ(x) for 0 ≤ x ≤ 20, and discuss the behavior of the function for positive and increasing x.

(b) ∫^∞ ₀ ƒ(x) dx is the area above the positive x-axis and under the infinitely many “humps” of the graph of ƒ. Compute this area.