University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

136

Pages:

1
Author:

Ciara Meyer

Workshop #25 To do the first two exercises, you need to know the following: Z b f (x)dx represents the area between the graph of y = f (x) and the x-axis, between x = a and x = b. a However, areas that are below the x-axis are counted as being negative. 1. Evaluate the following integrals by finding the corresponding areas. (a) R3 (b) R3 (c) R3 0 1 0 2xdx (x + 2)dx (x − 1)dx R4 0 (3 − 2x)dx R1 √ (e) −1 1 − x2 dx (d) 2. (a) Compute Ra (b) Compute Ra −a x 3 dx −a sin(x)dx (c) Below is a partial sketch of the graph of f (x). Complete the graph, so that value of a. (d) Find conditions on a function f (x) under which Ra 2 (e) Compute −a xex dx Ra −a f (x)dx (f) What property of a function g(x) would ensure that 3. Let f (x) = −a f (x) dx = 0 for any = 0 for all a. Rt −t g(x)dx x+1 x2 (a) Find the intervals on which f is increasing. (b) Identify any local maxima or minima. (c) Find the regions in which the graph of f is concave downward. (d) Find all inflection points for the graph of f . Ra =2 Rt 0 g(x)dx for every value of t?