Difference between revisions of "Nabla integral"
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| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>Theorem (Fundamental theorem of calculus):</strong> The following formula holds: |
$$\int_a^b f^{\nabla}(t) \nabla t = f(b)-f(a).$$ | $$\int_a^b f^{\nabla}(t) \nabla t = f(b)-f(a).$$ | ||
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Revision as of 16:23, 20 October 2014
Theorem: The following formula holds: $$\int_a^b f(t)+g(t) \nabla t = \int_a^b f(t) \nabla t + \int_a^b g(t) \nabla t$$
Proof: █
Theorem: The following formula holds: $$\int_a^b \alpha f(t) \nabla t = \alpha \int_a^b f(t) \nabla t$$
Proof: █
Theorem: The following formula holds: $$\int_a^b f(t) \nabla t = -\int_b^a f(t) \nabla t$$
Proof: █
Theorem: The following formula holds: $$\int_a^b f(t)\nabla t = \int_a^c f(t) \nabla t +\int_c^b f(t) \nabla t$$
Proof: █
Theorem: The following formula holds: $$\int_a^a f(t) \nabla t = 0$$
Proof: █
Theorem (Fundamental theorem of calculus): The following formula holds: $$\int_a^b f^{\nabla}(t) \nabla t = f(b)-f(a).$$
Proof: █
