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Math · Calculus
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1. There is a generalisation of the First Fundamental Theorem of Calculus which is named after Gottfried Wilhelm Leibniz [see the Just for fun! ox. If both the upper and lower limits of integration depend on the variable of differentiation, then Leibmizs Rule states that f(t) dt = f(v(z) -f(u(z)) dt초 dx Ju() (a) Prove this result and show that it simplifies to the First Fundamental Theorem of Calculus when u(z) and u(z) = a (a E R). (b) Find the value(s) of that minimises dt (c) Sketch a graph of the function f(a) to support your answer from part (b) Note: You should include information explaining how you arrived at the shape of the graph.

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