INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS Rational

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS Rational function: Example Find Example Find

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS Example Multiply by 1 Match coeff 2 subsitute The Heaviside 3 subsitute “Cover-up”

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS 1 2 3 Use long division Check if we can use subsitution Factor q(x) as linear factors or irreducible quadratic 4 q(x)= product of linear factor All distinct case 1 Some repeated case 2 Express p(x)/q(x) as a sum of partial fraction q(x)= product of quadratic (irred) All distinct case 3 repeated case 4

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of linear factor All distinct case 1 Some repeated case 2 Example Find

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of linear factor All distinct case 1 Example Find Some repeated case 2

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of quadratic (irred) All distinct case 3 Example repeated case 4

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS q(x)= product of quadratic (irred) Example All distinct case 3 repeated case 4 Example Expand by partial fraction Example Find

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS TERM-101 Solution:

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS

INTEGRATION OF RATIONAL FUNCTIONS BY PARTIAL FRACTIONS