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by: Rachel Klein


Rachel Klein
GPA 3.94

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About this Document

A concise, neat study that covers all information needed for the fourth exam for Math 125. It covers 11.1, 11.2, 11.3, 11.4, and 11.5
Basic Calculus 125
Study Guide
Math, Math125, Calculus, Precalculus, Integrals, Integration
50 ?




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This 2 page Study Guide was uploaded by Rachel Klein on Monday April 25, 2016. The Study Guide belongs to MATH 125 010 at University of Tennessee - Knoxville taught by in Spring 2016. Since its upload, it has received 30 views. For similar materials see Basic Calculus 125 in Math at University of Tennessee - Knoxville.


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Date Created: 04/25/16
Math 125 Basic Calculus Exam 4, Spring 2016 11.1 Antiderivatives and Integrals •! ! " #" = % " + ' Integral) sign) Differential) Integrand) Antiderivative) •! An integral is the opposite function of the derivative ( ! " #" = ! " + )' •! Integration Rules 1.! *#" = *" + ' 2.! *!(")#" = * ! " #" 3.! [! " + . " ]#" =) !(")#") +) . " #" 4.! [! " − . " ]#" =) !(")#") −) . " #" 1245 5.! 1 31 =) + 7, 2 ≠ 5 265 11.2 Integration by Substitution and General Power Rule 3: :245 •! : 2 31 =) : 3: =) + 7 31 265 1.! Identify a factor of u of the integrand that is raised to a power. Write down this factor as u = __________. ;< 2.! Then find and write down;=. 3.! Show that this derivative is also a factor of the integrand. 4.! If it is, then continue to the final step of the equation. 5.! If it is not, then manipulate the equation so that it is. ** remember that if you multiply something inside the integral, then you must divide by the same factor outside the integral. 11.3 Exponential and Logarithmic Integrals •! > 3: =)> + 7: , when u is a function of x. 5 3: •! 3: =) =) : ?5 =)@A : + 7 : : 11.4 The Fundamental Theorem •! If f(x) is non-negative and continuous in the interval [a,b], then C C B 1 31 = E 1 D = )E C ?)E(D) D o! Used to find the area under a curve •! Positive, Negative, and Nearly Zero F o! Positive:G! " #" > 0 o! Negative: F! " #" < 0 G F o! Nearly Zero:G ! " #" = nearly zero •! The Average Value of a Function o! 5 C B 1 31 C?D D 11.5 Area of a Region Bounded by 2 Graphs •! C B 1 ?H(1) 31) =)) C B 1 31?) C H 1 31 D D D o! In order to determine which function should be subtracted from which function, it is helpful to graph the functions in order to determine which function is located above the other. The one that is on top is the one that is used as f(x). •! Consumer Surplus = area between supply curve and price curve


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