Question

How to find all possible functions with the given derivative ? If

Answer 1

Answer:

a) $y = -\frac{1}{7}\cdot \cos 7\cdot t + C$, b) $y = -\frac{1}{7}\cdot \cos 7\cdot t + 7\cdot \sin \left(\frac{t}{7}\right) + C$.

Step-by-step explanation:

a) The antiderivative of $y' = \sin 7\cdot t$ is:

$y = -\frac{1}{7}\cdot \cos 7\cdot t + C$

b) The antiderivative of $y' = \sin 7\cdot t + \cos \left(\frac{t}{7}\right)$ is:

$y = -\frac{1}{7}\cdot \cos 7\cdot t + 7\cdot \sin \left(\frac{t}{7}\right) + C$