Calculate a definite integral using areas and properties of definite integrals.
I can determine when geometry should be used to evaluate a definite integral and do so accordingly.
I can apply appropriate integral properties to evaluate definite integrals.
Quick Lesson Plan
Instead of the traditional presentation of the rules for manipulating integrals, have your students derive the rules by working examples in context! Kallie burns calories on the treadmill so students can develop an understanding of the rules for adding integrands, multiplying integrands by a constant, and reversing the limits of integration.
After a fun conversation about New Year’s resolutions, students were motivated to follow Kaillie’s progress. Little direct intervention was required as groups reasoned through today’s Activity. Most students actually informally verbalized the appropriate rule of integration within their conversation while solving each problem! After writing the Activity margin notes as they apply to the given context, transitioning to the formal notation (Important Ideas) will be a simple task for most students.
Integration techniques are the basis for the second half of Calculus AB content. These skills are fundamental to success on both the multiple choice and free response sections. Any and all practice we can offer students throughout the rest of the course will improve their chances of scoring a 5 in May!
Many students forget that the vertical translation of a graph creates a rectangular area above or below the original region. The integral of the integrand “f(x) + k” cannot be found by simply integrating f(x) and then adding the constant k. See Activity #3 and Check Your Understanding #1d. Because students cannot have enough practice with certain skills, we have chosen to revisit the idea of opposites in CYU #2b and absolute value in CYU #2c.