# Calculus 2 exam 3

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 Author: AnnaRinaldo ID: 224902 Filename: Calculus 2 exam 3 Updated: 2013-07-08 01:40:49 Tags: Calculus Folders: Description: Calculus 2 Show Answers:

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1. What is 1/x2+1 dx?
Inverse tangent rule: tan-1x+c
2. What is a trig identity for sin2x?
Sin2x=2sinxcosx
3. What is a trig identity for cos2x?
Cos2x=(1+cos2x)/2
4. What is a trig identity for sin2x?
sin2x=(1-cos2x)/2
5. what is the anti-derivative of 1/u?
1/u= ln|u|+c
6. what is the anit-derivative of sec(u) du?
sec(u)du = ln|sec(u)+tan(u)|+c
7. What is the formula for integration by parts?
u dv = uv-vdu
8. what does ILATE stand for and what is it used for?
• I= inverse
• L= logarithm
• A= algebraic
• T= trig functions
• E= Exponentials
• *used to choose what "u" should be in integration by parts.
9. what is  secx dx?
sec(x) dx = ln|sec(x)+tan(x)|+c
10. u2-a2/u2 du equals?
= -u2-a2/u + ln|u+u2-a2|+c
11. cos-1udu equals?
= ucos-1u-(1-u2) +c
12. what is du/u(u2-a2) ?
=1/a sec-1 u/a +c
13. How do you complete the square?
(ax2+bx+c) = (ax2+bx+(b/2)2) -(b/2)2+c
14. what is 1/(a2-u2) du?
= sin-1(u/a)+c
15. What is
sin2(x)dx?
= x/2 - sin(2x)/4 +c
16. what is cos2(x)dx ?
= x/2 + sin(2x)/4 +c
17. u2 ln(u) du ?
= un+1 / (n+1)[(n+1)ln(u)-1] +c
18. what is the derivative of 1/(x2+1)?
= tan-1x+c
19. (a2+u2)/ udu?
= (a2+u2)/u + ln(u+(a2+u2)) +c
20. what do you do when the top is longer than the bottom on the integral of polynomials?
long divide the bottom from the top first.

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