MATH231 Lecture Notes

MATH231 Lecture Notes - Lecture 3:: Trigonometric...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 3:: Trigonometric Substitutions Revisited 0.1 Reduction Formulae: One idea which is useful is that of a reduction formula. The basic idea is to reduce an integral to a similar integral of lower order. For example: to compute R sin n ( x ) we might do the following Z sin n ( x ) dx =- cos( x ) sin n- 1 ( x ) + ( n- 1) Z cos 2 ( x ) sin n- 1 ( x ) dx n Z sin n ( x ) dx =- cos( x ) sin n- 1 ( x ) + ( n- 1) Z sin n- 1 ( x ) dx Z sin n ( x ) dx =- 1 n cos( x ) sin n- 1 ( x ) + n- 1 n Z sin n- 2 ( x ) dx Thus we can relate R sin 2 ( x ) dx to R sin ( x ) dx = R dx , R sin 4 ( x ) dx to R sin 2 ( x ) dx. Similarly for odd powers we find that we can relate R sin 3 ( x ) dx to R sin( x ) dx , R sin 5 ( x ) dx to R sin 3 ( x ) Self Study Problems: Compute R sin 6 ( x ) dx using the above reduction formula. Derive an analogous reduction formula for R cos n ( x ) dx . 0.2 General Trig Substitutions: To start with I will calculate a couple of integrals well use a bunch of times in...
View Full Document

Page1 / 3

MATH231 Lecture Notes - Lecture 3:: Trigonometric...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online