Integration by Parts Text Reference: Section 5.4, p. 330 The purpose of this set of exercises is to show how the matrix of a linear transformation relative to a basis B may be used to find antiderivatives usually found using integration by parts. To find Jt2er dt, the normal approach would be to integrate by parts twice, and find that 2tet 2et C t e' dt t e However, near algebra can be used to solve this problem. Look at the set B {t er, te', e'). This set may be shown to be nearly independent by the method used in Exercise 37 in Section 4.3 start by assuming that This equation must hold true for all real t Choose three specific values for t: 0,1, and 2. This generates the following system of equations eco EC3
Show transcribed image text Integration by Parts Text Reference: Section 5.4, p. 330 The purpose of this set of exercises is to show how the matrix of a linear transformation relative to a basis B may be used to find antiderivatives usually found using integration by parts. To find Jt2er dt, the normal approach would be to integrate by parts twice, and find that 2tet 2et C t e' dt t e However, near algebra can be used to solve this problem. Look at the set B {t er, te', e'). This set may be shown to be nearly independent by the method used in Exercise 37 in Section 4.3 start by assuming that This equation must hold true for all real t Choose three specific values for t: 0,1, and 2. This generates the following system of equations eco EC3