Calculus‎ > ‎

### Integral Evaluation

 Riemann Sum1) Estimating the area under a curve with a graphExplanation:Notes | AnnotatedWebsites:Interactive website by ShodorInteractive website by teacherlinkType in any function for Riemann sums website2) Estimating the area under a curve with a functionExplanation:Notes | AnnotatedPractice ProblemsWorksheet | Answers3) Estimating the area under a curve with a tableExplanation:Notes | AnnotatedPractice ProblemsWorksheet | Answers4)  Find the area under a curve when it is an exact geometric shape & Integral NotationExplanation:Notes | AnnotatedPractice ProblemsWorksheet | Answers5)  Estimating the area under a curve using the Trapezoidal RuleExplanation:Notes | AnnotatedPractice ProblemsWorksheet | Answers6)  Over and Under EstimatesExplanation:Notes | AnnotatedPractice ProblemsWorksheet | Answers7) Integral PropertiesExplanation:Practice ProblemsWorksheet | Answers8) Review approximation methods and integral propertiesPractice Problems9) First Semester Review Worksheet | AnswersAntiderivatives and Indefinite Integrals10) Basic antiderivatives (power rule; basic trig)Explanation:Notes | AnnotatedTrig Review Handout (includes trig identities, derivatives, and antiderivatives)Wolfram Alpha Indefinite Integral CalculatorVideos: Hollis: Antiderivative and Indefinite Integrals - slides 1-8Khan: The indefinite integral or antiderivativeKhan: Indefinite Integrals (part II) : polynomialsPractice Problems:Antiderivatives WS | Answers11)  Review Basic antiderivativesExplanation:Practice Problems:12) Particular Solution/Initial ValueExplanationNotes | AnnotatedVideo: Hollis: Antiderivative and Indefinite Integrals - slide 9Practice Problems:Particular Solution WS | Answers13)  U-Substitution with Indefinite Integrals with PowersExplanation:Notes | AnnotatedVideos:Khan: Definite Integrals (part 4)Hollis: Change of Variables (Substitution) - slides 1-7Definite Integrals with U-Sub Kahn video - Indefinite Integration (part III) - more of an intuitive approach for reverse of the chain rule than using u-subHollis: The Natural Log: - watch slides 6 and 7Practice Problems:Worksheet | Answers14)  U-Substitution with Indefinite Integrals with Exponential and TrigExplanation:Videos:Youtube | TeachertubeHollis: The exponential function: watch slide 3 & 4Practice Problems:15) Mixed Review of Indefinite Integrals16) Double U-SubNotesDefinite Integrals:  Fundamental Theorem of Calculus (FTC) - evaluation part: 17) Definite Integrals with antiderivative rules Explanation:Notes | Annotated18)  With U-Sub: Explanation:Notes | AnnotatedVideo: Hollis: Change of Variables (Substitution) - slides 8-9Khan: Definite integral with substitutionPractice Problems19) Using Definite Integrals with Integral PropertiesExplanation:Notes | Annotated Practice Problems:20) Antiderivative of Derivatives Explanation:Notes | AnnotatedPractice Problems:21) Integral of Piecewise functionsExplanationNotes | AnnotatedPractice Problems22)  Using Your calculator to approximate definite Integrals23)  Average Value of a FunctionExplanation:Notes | AnnotatedPractice Problems:Desmos Activity: Average Value of a Function (teacher use only)Worksheet | Answers24)  Integral Review WS | Answers2012 Q1 - given a table: average rate of change, average value - parts a, b, and c2011 (Form B) Q6 - part a: integral evaluation2011(Form B) Q2 - given a piecewise function: average rate, instantaneous rate of change2011 (Form B) Q1 - given a function: net change, average rate of change, existence2011 Q6 - given a piecewise function: evaluate a definite integral2010 Q2 - given a table and equation: average rate, average value2009 Q5 - given a table: average rate, left Riemann sum2008 (Form B) Q3 - given a table and equation: trap sum, average value, net change2005 Q3 - given a table: average rate, average value, trap2004 Q1 - given an equation:  net change, average value, average rate2003 (Form B) Q3 - given a table: average rate, midpoint sum2003 Q3 - given a table and graph: rates, average value, left Riemann sum2001 Q5 - part b - solve for a constant given  a definite integral2001 Q2 - given a table and equation: trap sum, average rate, average value, instantaneous rate1999 Q3 - given a table and equation: midpoint sum, average value26)  Cumulative Review WS | Answers