Question 1. Compute the area between y = 1 - x and y = 1-x. Question...

Transcribed Image Text:

Question 1. Compute the area between y = 1 - x and y = 1-x. Question 2. What is the volume of the solid formed by rotating the region in Question 1 about x-axis using washer method? Question 1. Consider the integral f(x)dx, where f(x) = cos (x). a) Expand the integral as a series and determine how many terms are nec- essary to approximate the integral to within 10-2. Hint: First integrate the series, then note that the new series is alter- nating. Recall that the Maclaurin series for cos x = (1) n=0 (2n)! b) Determine how many (equal) sub-intervals are necessary to approximate the integral to within 10-2 using trapezoid rule. Hint: f'(x)=sin (x2)2x and f"(x) = 2(2x cos (x) + sin (x)). And ET K(b-a) where f"(x)| K for a < x < b. 12n2 Question 1. Compute the area between y = 1 - x and y = 1-x. Question 2. What is the volume of the solid formed by rotating the region in Question 1 about x-axis using washer method? Question 1. Consider the integral f(x)dx, where f(x) = cos (x). a) Expand the integral as a series and determine how many terms are nec- essary to approximate the integral to within 10-2. Hint: First integrate the series, then note that the new series is alter- nating. Recall that the Maclaurin series for cos x = (1) n=0 (2n)! b) Determine how many (equal) sub-intervals are necessary to approximate the integral to within 10-2 using trapezoid rule. Hint: f'(x)=sin (x2)2x and f"(x) = 2(2x cos (x) + sin (x)). And ET K(b-a) where f"(x)| K for a < x < b. 12n2