MATH 1172 Quiz: MATH 1172 Ohio State University Math 1172 Au2014 Quiz 4 Solutions

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

Z x2 + 3x + 4 x3 + 2x2 + 2x dx. Solution: the denominator factors as x(x2 + 2x + 2). We know x2 + 2x + 2 is irreducible since 22 4 1 2 = 4 < 0. Thus the general form of the partial fraction decomposition for x2+3x+4 x3+2x2+2x is. X2 + 3x + 4 x3 + 2x2 + 2x. Bx + c x2 + 2x + 2 where a, b, c are unknown constants. After multiplying through by the denominator, we have that. X2 + 3x + 4 = a(x2 + 2x + 2) + (bx + c)x. By plugging in x = 0, we have. 02 + 3 0 + 4 = a(02 + 2 0 + 2) + (b 0 + c)0. In other words 4 = 2a and a = 2. In order to nd b and c we will need to pass to a system of linear equations.