understand when the antiderivative so Understand and use the Second represented is continuous and Fundamental Theorem of Calculus. differentiable. Apply basic properties of definite integrals. Domain: Calculate and Apply Integrals Objectives: 4.5: Integration by Substitution Cluster: Apply techniques of antidifferentiation Students will: Use pattern recognition to find an indefinite Additional Resource(s) integral. Use change of variables to find an indefinite Develop facility with finding Larson Calculus Videos Section 4.5 – integral. antiderivatives that follow directly from derivatives of basic functions (power, Use the general power rule for integration to exponential, logarithmic, and find an indefinite integral. trigonometric). Use a change of variables to evaluate a Khan Academy Calculus Videos Use substitution of variables to calculate definite integral. antiderivatives (including changing limits Evaluate a definite integral involving an even for definite integrals). or odd function. Find specific antiderivatives using initial conditions. 4.6: Numerical Integration Domain: Understanding Integrals Objectives: Demonstrate understanding of a Students will: Cluster: Additional Resource(s) Definite Integral Approximate a definite integral using the Trapezoidal Rule. Larson Calculus Videos Section 4.6 – 3. Use Riemann sums (left, right, and midpoint) and trapezoidal sums to approximate definite integrals of functions, represented graphically, numerically, and by tables of Khan Academy Calculus Videos values.
understand when the antiderivative so represented is continuous and differentiable. Apply basic properties of definite integrals. Understand and use the Second Fundamental Theorem of Calculus. Domain: Calculate and Apply Integrals Cluster: Apply techniques of antidifferentiation Develop facility with finding antiderivatives that follow directly from derivatives of basic functions (power, exponential, logarithmic, and trigonometric). Use substitution of variables to calculate antiderivatives (including changing limits for definite integrals). Find specific antiderivatives using initial conditions. Objectives: Students will: Use pattern recognition to find an indefinite integral. Use change of variables to find an indefinite integral. Use the general power rule for integration to find an indefinite integral. Use a change of variables to evaluate a definite integral. Evaluate a definite integral involving an even or odd function. 4.5: Integration by Substitution Additional Resource(s) Larson Calculus Videos – Section 4.5 Khan Academy Calculus Videos Domain: Understanding Integrals Cluster: Demonstrate understanding of a Definite Integral 3. Use Riemann sums (left, right, and midpoint) and trapezoidal sums to approximate definite integrals of functions, represented graphically, numerically, and by tables of values. Objectives: Students will: Approximate a definite integral using the Trapezoidal Rule. 4.6: Numerical Integration Additional Resource(s) Larson Calculus Videos – Section 4.6 Khan Academy Calculus Videos
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