Final answer:
To evaluate the line integral of f = 2sin(x), substitute the values into the line integral formula and simplify before integrating to obtain the numerical value.
Step-by-step explanation:
To evaluate the line integral of the function f = 2sin(x), we need to integrate f along a given path. Let's suppose the path is represented by a parameter t, and we have a parametric representation of the path as x = x(t) and y = y(t). The line integral can be evaluated using the formula:
L = ∫ f(x(t), y(t)) ⋅ sqrt[(dx/dt)^2 + (dy/dt)^2] dt
In this case, since we have f = 2sin(x) and x = x(t), we substitute these values into the formula:
L = ∫ 2sin(x(t)) ⋅ sqrt[(dx/dt)^2 + (dy/dt)^2] dt
Simplify and integrate the expression to obtain the numerical value of the line integral.