PP 8.3 - Trigonometric Substitutions Working with Right...

Info iconThis preview shows pages 1–6. 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

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

View Full DocumentRight 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: Trigonometric Substitutions Working with Right Triangles a 2 2 b a + a b a c 2 2 a c- When the square root contains a difference, it represents a leg. When the square root contains a sum, it represents the hypotenuse. In this Section We will learn to evaluate integrals that involve either the sum or the difference of squares. We will use the following facts: hypotenuse side opposite sin = A A side adjacent side opposite tan = A side adjacent hypotenuse sec = A Examples dx x ∫- 2 4 . 1 2 4 x- θ There is no integration formula for this integral and no u-substitution can be used. The difference of squares under the radical indicates that a right triangle can be used. 2 x If the variable is opposite to an acute angle, we should select that angle to work with. θ θ sin 2 2 sin = ⇒ = x x θ θ sin 2 2 sin = ⇒ = x x Since we will be replacing x by an expression involving a trigonometric function, we are making a trigonometric substitution. θ θ θ θ θ cos 2 4 2 4 cos cos 2 sin 2 2 2 =- ⇒- = = ⇒ = x x d dx x dx x ∫- 2 4 ∫ ∫ ∫ = =- ⇒ θ θ θ θ θ d d dx x 2 2 cos 4 cos 2 cos 2 4 Once the trigonometric substitution is complete, we obtain a trigonometric integral, as the ones studied in the last section. [ ]...
View Full Document

This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.

Page1 / 18

PP 8.3 - Trigonometric Substitutions Working with Right...

This preview shows document pages 1 - 6. Sign up to view the full document.

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