reduction formulas

To obtain a reduction formula for sinnxcosmxdx :

- Split off sinx to integrate by parts


Take u=sinn-1xcosmx, and dv=sinxdx So du=[(n-1)sinn-2xcosm+1x-msinnxcosm-1x]dx, and v=-cosx
- Then simplify to get

- Now use the identity sin2x+cos2x=1 in the middle term and simplify to get

- Take the last two integrals to the left side:

- Since [1+(n-1)+m]=m+n divide both sides by m+n and hence


Using the exact same method but instead of splitting off sinx , one can split off cosx and follow similar procedure to obtain another reduction formula:


Title reduction formulas
Canonical name ReductionFormulas
Date of creation 2013-03-22 17:37:06
Last modified on 2013-03-22 17:37:06
Owner curious (18562)
Last modified by curious (18562)
Numerical id 9
Author curious (18562)
Entry type Definition
Classification msc 26A36
Synonym powers of sines and cosines
Synonym integration of trigonometric functions
Related topic TrigonometricFormulasFromDeMoivreIdentity