6: Using Definite Integrals Last updated Apr 4, 2022 Save as PDF Fundamental Trigonometric Identities Default Text Page ID4333 ( \newcommand{\kernel}{\mathrm{null}\,}\) An Introductory Calculus Libretexts Textmap Active Calculus by Matt Boelkins, David Austin, and Steve Schlicker Chapter 1 Chapter 1: Understanding the Derivative 1.1: How do we Measure Velocity? 1.2: The Notion of Limit 1.3: The Derivative of a Function at a Point 1.4: The Derivative Function 1.5: Interpretating, Estimating, and Using the Derivative 1.6: The Second Derivative 1.7: Limits, Continuity, and Differentiability 1.8: The Tangent Line Approximation 1.E: Understanding the Derivative (Exercises) • Chapter 2 Chapter 2: Computing Derivatives 2.1: Elementary Derivative Rules 2.2: The Sine and Cosine Function 2.3: The Product and Quotient Rules 2.4: Derivatives of Other Trigonometric Functions 2.5: The Chain Rule 2.6: Derivatives of Inverse Functions 2.7: Derivatives of Functions Given Implicitely 2.8: Using Derivatives to Evaluate Limits 2.E: Computing Derivatives (Exercises) • Chapter 3 Chapter 3: Using Derivatives 3.1: Using Derivatives to Identify Extreme Values 3.2: Using Derivatives to Describe Families of Functions 3.3: Global Optimization 3.4: Applied Optimization 3.5: Related Rates 3.E: Using Derivatives (Exercises) • Chapter 4 Chapter 4: The Definite Integral 4.1: Determining Distance Traveled from Velocity 4.2: Riemann Sums 4.3: The Definite Integral 4.4: The Fundamental Theorem of Calculus 4.E: The Definite Integral (Exercises) • Chapter 5 Chapter 5: Finding Antiderivatives and Evaluating Integrals 5.1: Construction Accurate Graphs of Antiderivatives 5.2: The Second Fundamental Theorem of Calculus 5.3 Integration by Substitution 5.4: Integration by Parts 5.5: Other Options for Finding Algebraic Derivatives 5.6: Numerical Integration 5.E: Finding Antiderivatives and Evaluating Integrals (Exercises) • Chapter 6 Chapter 6: Using Definite Integrals 6.1: Using Definite Integrals to Find Area and Length 6.2: Using Definite Integrals to Find Volume 6.3: Density, Mass, and Center of Mass 6.4: Physics Applications: Work, Force, and Pressure 6.5: Improper Integrals 6.E: Using Definite Integrals (Exercises) • Chapter 7 Chapter 7: Differential Equations 7.1: An Introduction to Differential Equations 7.2: Qualitative Behavior of Solutions to Differential Equations 7.3: Euler's Method 7.4: Separable Differential Equations 7.5: Modeling with Differential Equations 7.6: Population Growth and the Logistic Equation 7.E: Differential Equations (Exercises) • Chapter 8 Chapter 8: Sequences and Series 8.1: Sequences 8.2: Geometric Series 8.3: Series of Real Numbers 8.4: Alternating Series 8.5: Taylor Polynomials and Taylor Series 8.6: Power Series 8.E: Sequences and Series (Exercises) Template:HideTOC