MATH 1300 Quiz: MATH1300 Quiz 10 2015 Fall

• School: CU-Boulder
• Department: Mathematics
• Course: MATH 1300
• Professor: All

Document Summary

This quiz is due monday, april 26th in class. Show all your work: evaluate the following de nite integrals (x3 x)dx we have (cid:90) 1. You may also note that the integral is zero because x3 x is odd and [ 1, 1] is symmetric about the y-axis (see picture below). (a) (b) y. 1 x3 x is negative on [ 1, 0] and positive on [0, 1] so that (cid:26) x3 x x [ 1, 0] x x3 x [0, 1] |x3 x|dx = (x3 x)dx + (x x3)dx (cid:90) 0 (cid:20)x4 (cid:18) 2 (cid:90) (cid:90) (cid:90) (c) (d) (sin x x)dx. We have (sin x x)dx = cos x x2. 2 (once again, sin x x is odd and [ , ] is symmetric about the y-axis. ) | sin x|dx sin x is negative on [ , 0] and positive on [0, ] so that (cid:26) sin x x [ , 0] sin x x [0, ]