Properties

Theorem: The following formula holds: $$\int_a^a f(t) \Diamond t=0.$$

Proof: █

Theorem: The following formula holds: $$\int_a^b f(t) \Diamond t= \int_a^c f(t) \Diamond t + \int_c^b f(t) \Diamond t.$$

Proof: █

Theorem: The following formula holds: $$\int_a^b f(t) \Diamond t= -\int_b^a f(t) \Diamond t.$$

Proof: █

Theorem (Sum Rule): The following formula holds: $$\int_a^b (f+g)(t) \Diamond t= \int_a^b f(t) \Diamond t + \int_a^b g(t) \Diamond t.$$

Proof: █

Theorem (Constant Multiple): The following formula holds: $$\int_a^b \alpha f(t) \Diamond t= \alpha \int_a^b f(t) \Diamond t.$$

Proof: █

References