References: TN State Standards Content Instructional Support & Resources Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions Chapter 6: Differential Equations (Allow approximately 4 - 5 weeks for instruction, review, and assessment) Chapter 5 Vocabulary (5-5 & 5-7) Domain: Calculate and Apply Integrals Enduring Understandings: 5.5: Other than e and Applications Base, exponential function to the base a, Cluster: Apply techniques of differentiation Derivatives and anti-derivatives have an 5.7: Inverse Trigonometric Functions: logarithmic function to the base a, separation inverse relationship to each other. Integration of variables The area under the curve is the geometric Develop facility with finding meaning of anti-derivatives. antiderivatives that follow directly from Additional Resource(s) The anti-derivative has both theoretical derivatives of basic functions (power, Larson Calculus Videos Section 5.5 – and real life applications. exponential, logarithmic, and Larson Calculus Videos Essential Questions: trigonometric). How are the for differentiation used to Video Bases Other than e and Applications – develop the basic rules of integration? How can we use the measure of area s under a curve to discuss net change of a function over time? How are area under the curve and the definite integral related? Objectives: Students will: Integrate exponentials that have bases other than e.
References: TN State Standards Content Instructional Support & Resources Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions Chapter 6: Differential Equations (Allow approximately 4 - 5 weeks for instruction, review, and assessment) Domain: Calculate and Apply Integrals Cluster: Apply techniques of differentiation Develop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric). Enduring Understandings: Derivatives and anti-derivatives have an inverse relationship to each other. The area under the curve is the geometric meaning of anti-derivatives. The anti-derivative has both theoretical and real life applications. Essential Questions: How are the for differentiation used to develop the basic rules of integration? How can we use the measure of area under a curve to discuss net change of a function over time? How are area under the curve and the definite integral related? Objectives: Students will: Integrate exponentials that have bases other than e. 5.5: Other than e and Applications 5.7: Inverse Trigonometric Functions: Integration Additional Resource(s) Larson Calculus Videos – Section 5.5 Larson Calculus Videos Video – Bases Other than e and Applications s Chapter 5 Vocabulary (5-5 & 5-7) Base, exponential function to the base a, logarithmic function to the base a, separation of variables