Answer:
The function is [tex]-\sin x[/tex] and the constant of integration is [tex]C = - 1[/tex].
Explanation:
The resultant expression is equal to the sum of a constant multiplied by the integral of a given function and an integration constant. That is:
[tex]a = k\cdot \int\limits {f(x)} \, dx + C[/tex]
Where:
[tex]k[/tex] - Constant, dimensionless.
[tex]C[/tex] - Integration constant, dimensionless.
By comparing terms, [tex]k = 2[/tex], [tex]C = -1[/tex] and [tex]\int {f(x)} \, dx = \cos x[/tex]. Then, [tex]f(x)[/tex] is determined by deriving the cosine function:
[tex]f(x) = \frac{d}{dx} (\cos x)[/tex]
[tex]f(x) = -\sin x[/tex]
The function is [tex]-\sin x[/tex] and the constant of integration is [tex]C = - 1[/tex].
