MAT 132 Midterm: MAT 132 SBU Exam Solution 2

• School: Stony Brook University
• Department: Mathematics
• Course: MAT 132
• Professor: All

Document Summary

2 (a) find the average value of f on the interval [ 1, 1]. The average value of f on [a, b] is. 1 e(cid:19) = 1. 752 . (b) find the length of y = f (x) from x = 1 to x = 1. Solve the di erential equation y = y cos x. 1 + y2 subject to the initial condition y(0) = 1. 1 + y2 y dy = cos(x)dx z 1 y. + y dy =z cos(x) dx ln(y) + The condition that y(0) = 1 means that c satis es ln(1) + So, we have y satis es the equation ln(y) + Sketch the solution curves to the di erential equation y = x y. Y dy = x dx y2. + c x2 + y2 = 2c. So, the solution curves are all circles centered at the origin.