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Unformatted text preview: M 408L Integral Calculus prepared by Chris Mirabito Test #1 Review Test #1 will be held on Tuesday, Februaray 20th, 2007 from 7:00pm until 9:00pm in ETC 2.108 Please bring your UT ID cards to the test. We will be checking them: your cooperation with the University policy on cheating is expected. Also, remember to bring a #2 pencil and eraser to the test, as none will be provided. All other testing materials will be provided. This review sheet is intended to help you prepare for the test. It states in a nutshell pretty much everything that we have covered in the course thus far, but this list is not exhaustive . Please be sure you are familiar with all concepts listed here. If you are having trouble, please stop by your Instructor’s or your TA’s office hours. Do not wait until the last minute to ask for help. w Students with legitimate, documented learning disabilities or special needs should consult the “First Day Handout” located at http://www.ma.utexas.edu/dev/math/Courses/M408L/handout.html for information regarding testing dates, times, and locations (which will be different from that of the regular time). Students who cannot take the test at the regularly scheduled time due to conflicts with other classes, exams, or docu- mented illnesses should also consult this page for make-up test information. In all cases, make sure Dr. Fouli knows about your situation well in advance. § 4.10 Antiderivatives • Remember that you need to antidifferentiate. Do NOT take derivatives. • C is for coffee (you need it to stay awake just like you need this in your antiderivative!). • You need to solve for C if you are given initial conditions (like f ( ) = 1 , f ( 2 ) = 3 , etc.). • For the motion problems, remember that s 00 ( t ) = v ( t ) = a ( t ) , and that speed = | v ( t ) | . • Remember your trigonometric identities! Don’t be fooled if you are asked to antidifferentiate sec 2 x- tan 2 x . • Pay attention to the graphs of all possible antiderivatives for f ( x ) . Remember that all differ only by a constant. § 5.1 Areas and Distances • Recall the formulas x = a , x i = a + i ∆ x , x n = b . • For practice you may want to try #14 in this section. I did this one with my section a few semesters ago. It’s interesting and it will help you learn this material. § 5.2 The Definite Integral • Riemann Sums: You can find ∆ x using the formula ∆ x = b- a n , where b is the right endpoint, a is the left endpoint, and n is the number of subintervals you are using. Some tips: 1. Since all the ∆ x ’s are the same, you can write the sum as ∆ x [ f ( x 1 ) + ··· + f ( x n )] . 2. To check your work, using any of the 3 rules ( Left Endpoint Rule , Right Endpoint Rule , or Midpoint Rule ) make sure you have n terms inside the brackets....
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- Fall '07