Answer:
a) [tex]y = -\frac{1}{7}\cdot \cos 7\cdot t + C[/tex], b) [tex]y = -\frac{1}{7}\cdot \cos 7\cdot t + 7\cdot \sin \left(\frac{t}{7}\right) + C[/tex].
Step-by-step explanation:
a) The antiderivative of [tex]y' = \sin 7\cdot t[/tex] is:
[tex]y = -\frac{1}{7}\cdot \cos 7\cdot t + C[/tex]
b) The antiderivative of [tex]y' = \sin 7\cdot t + \cos \left(\frac{t}{7}\right)[/tex] is:
[tex]y = -\frac{1}{7}\cdot \cos 7\cdot t + 7\cdot \sin \left(\frac{t}{7}\right) + C[/tex]
