Section 5_7 Ma141

# Section 5_7 Ma141 - Section 5.7 More techniques of...

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Section 5.7 More techniques of Integration I. Trigonometric Integrals II. Partial Fractions III. Trigonometric Substitution ( we’ll cover this after the test) I. Integrals involving Trigonometry Must “play around with” to work out; remember your trig. identities and your rules of derivatives with trigonometry Common Identities that come up with these: Pythagorean Identities cos 2 x + sin 2 x = 1 tan 2 x + 1 = sec 2 x cot 2 x + 1 = csc 2 x Double angle formulas sin2 x = 2sin x cos x cos2 x = cos 2 x " sin 2 x = 1 " 2 x = 2cos 2 x " 1 tan2 x = 2tan x 1 " tan 2 x Half-Angle formulas sin 2 ( x 2 ) = 1 " cos x 2 cos 2 ( x 2 ) = 1 + cos x 2 Example 1: sin 5 xdx " Example 2: cos 2 xdx " Example 3 : tan 2 x sec 4 xdx 0 " / 4 #

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II. Partial Fractions Decomposing fractions Please read notes on page 392 Note 1 long division Note 2 more than one linear factor

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## This note was uploaded on 01/25/2012 for the course MA 241 taught by Professor Mccollum during the Spring '08 term at N.C. State.

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Section 5_7 Ma141 - Section 5.7 More techniques of...

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