calculus assignment

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fnen1994

Mathematics

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please answer these questions showing all steps

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Math 273 Assignment 11 Due Date: December ¡++¿ Assignment 1. Compute each of the following definite integrals by applying the Fundamental Theorem of Calculus Part Two. Z 5 (x − 2)(5 − x) dx (a) 2 Z π sin2 (x) dx (b) −π R 11 2. Suppose that f is continuous on the interval [4, 11] and that 4 f (x) dx = 35. Explain why there must be a number c in the interval [4, 11] so that f (c) = 5. R x2 3. Let g(x) = 0 f (t) dt, where f is the function whose graph is displayed below. Compute g 0 (3). 4. Determine whether the following statements are true or false; justify your answer. (a) If the function F (x) is an antiderivative of a function f (x), then Z b f (x) dx = F (b) − F (a). a (b) If a function f (x) is continuous on [a, b], then the area enclosed by the graph of y = f (x), y = 0, x = a and x = b equals (numerically) Z b f (x) dx. a (c) If u = g(x) is a differentiable function whose range is an interval I and f is continuous on I, then Z Z  0 f g(x) g (x) dx = f (u) du. Version 2 Page 1 of 1 Last revised November 30, 2018
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