Reference no: EM131369739
The Fundamental Theorem of Calculus
(1) Below is the part of the graph of a function f(t). Let F(x) = 0∫x f(t)dt
(a) Find F(4.5).
(b) Find F'(4.5).
(c) Find F"(4.5).
(d) Find the minimum and maximum values of F(x) on [0, 5].
(e) Suppose it is given that -2∫2f(t)dt = 5. Find -2∫-1f(t)dt.
(2) Suppose that f is a continuous function and that f(3) = 3, f(6) = 5.
Let G(x) = 1∫x^2f(t)dt. Find G'(3).
(3) Suppose that f is a continuous function and that f(1) = 1, f(3) = -4.
Let H(x) = x∫10f(t)dt. Find H'(2).
(4) Suppose that f is a continuous function and that f(2) = 5, f(3) = 2,
Let K(x) = √x∫xf(t) dt. Find K'(4).
(5) Suppose F'(x) = f(x) and we are given F(1) = 10, F(2) = 5, F(10) = 1.
Find 1∫5f(x)dx.
(6) Find x such that -1∫x (1/1+t2)dt = (7π/12).
I need all the steps and finish.
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