Integration of Trigonometric Polynomials Integrals of the type
- Slides: 9
Integration of Trigonometric Polynomials Integrals of the type Case 1: n is odd Case 2: m is odd Case 3: both m and n are even General Trigonometric Polynomials Index FAQ
Basic Trigonometric Monomials 1 Problem Example This computation was possible since the function to be integrated was a (simple) polynomial in the sine function times the cosine function. Index Mika Seppälä: Integration by Substitution FAQ
Basic Trigonometric Monomials 2 Problem Case 1: n is odd. If n = 2 k+1 is odd then one can rewrite the function to be integrated using the formula This can be reduced to an integral of a polynomial by the substitution t = sin(x). Index Mika Seppälä: Integration by Substitution FAQ
Basic Trigonometric Monomials 3 Example Solution Rewrite The last integral is easy to compute. One gets Index Mika Seppälä: Integration by Substitution FAQ
Basic Trigonometric Monomials 4 Problem Case 2: m is odd If m = 2 k+1 is odd then one can rewrite the function to be integrated using the formula This can be reduced to an integral of a polynomial by the substitution t = cos(x). Index Mika Seppälä: Integration by Substitution FAQ
Basic Trigonometric Monomials 5 Example Solution Rewrite The last integral is easy to compute. One gets Index Mika Seppälä: Integration by Substitution FAQ
Basic Trigonometric Monomials 6 Problem Case 3: m and n even If both m and n are even use the trigonometric formulae to simplify the function to be integrated. Index Mika Seppälä: Integration by Substitution FAQ
Basic Trigonometric Monomials 7 Example Solution Now use the same trig formula again! Index Mika Seppälä: Integration by Substitution FAQ
Integration of Trigonometric Polynomials Problem Solution Index Mika Seppälä: Integration by Substitution FAQ
