This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: M10360 Exam 3: Review Guide Chapter 8 8.3 Trigonometric Integrals Know the main identities: 1. sin 2 x + cos 2 x = 1 2. sin 2 x = 1 cos(2 x ) 2 3. cos 2 x = 1 + cos(2 x ) 2 4. tan 2 x + 1 = sec 2 x Understand how to split off cosines, sines, secants and tangents to be able to use one of the above identities along with a usubstitution. 8.5 Partial Fractions Know how to split up a fraction into its partial fraction decomposition. Follow the steps given below: 1. Make sure the numerator has smaller degree than the denominator. Otherwise, do long division. 2. Remember to factor the denominator completely . Combine linear and irre ducible quadratic terms. Repeated linear terms are of the form ( px + q ) m . Repeated irreducible quadratic terms are of the form ( ax 2 + bx + c ) n . A quadratic is irreducible if b 2 4 ac < 0. 3. For each repeated linear term ( px + q ) m , we get m fractions in the decomposition of the form: A ( px + q ) + B ( px + q ) 2 + + D ( px + q ) m (notice linear terms, even though repeated, get constants in the numerator) and for each repeated irreducible quadratic term ( ax 2 + bx + c ) n , we get n fractions in the decomposition of the form Ax + B ( ax 2 + bx + c ) + Cx + D ( ax 2 + c ) 2 + + Ex + F ( ax 2 + bx + c ) n (notice irreducible quadratic terms all get linear terms in the numerator). After doing the decomposition, readd the fractions and set the numerators equal. This will give you a bunch of equations based on coefficients of x,x 2 and the constant term. Use these equations to solve for the unknown parameters, A , B , C , etc....
View
Full
Document
 Spring '08
 Edgar
 Calculus, Integrals

Click to edit the document details