This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: able to compute both types. The following identities will be given to you on the exam. I might even put more if I’m feeling generous! • sin 2 x + cos 2 x = 1 • tan 2 x + 1 = sec 2 x • cos 2 x = 1 2 (1 + cos(2 x )) • sin 2 x = 1 2 (1cos(2 x )) • sin(2 x ) = 2 sin( x ) cos( x ) Techniques you need to know: • usubstitution. For example, Z x ( x 2 + 1) 3 dx See Stewart 5.5 for more. • Integration by parts. For example, Z x sin( x ) dx See Stewart 7.1 for more. • Partial fractions. For example, Z x 2 + 3 x 32 x 23 x dx See Stewart 7.4 for more. • Inverse/trigonometric substitutions. For example, Z 1 x 2 √ x 216 dx See Stewart 7.3 for more. • Strategy for integrating i.e., identifying which of the above techniques to apply to a given integral and combining the above techniques to compute integrals. See Stewart 7.5. • You also need to know about improper integrals. For example Z ∞ 2 1 x 2 dx See Stewart 7.8 for more....
View
Full Document
 Spring '08
 Shu
 Calculus, calculus book, Math 3B Midterm

Click to edit the document details