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ResourceSpotlight
In this activity, students will use integration by parts to integrate ln x. In the homework/extension problems, they will use a similar process to integrate tan-1x. Self-check questions engage students and help deepen understanding. Multiple-choice exam-like questions are also included to apply what was learned. Additionally, students will review integration using substitution.
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Texas Instruments, Inc.
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ResourceSpotlight
Students will explore Riemann sums to approximate the area under the graph of y = x2 on the interval [0, 1]. They will use the Rectangle tool to draw left-endpoint, right-endpoint, and midpoint approximating rectangles. Students will write area formulas in expanded form and summation notation and analyze how their approximations compare to the exact area. Students will use these findings to understand that an infinite number of approximating rectangles will yield the exact area under a curve.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will be introduced to the concept of finding the volume of a solid formed by cross sections of a function that form certain shapes. Since volume is the area of the base times the height and dV = Area dx, student review areas of various shapes like squares, semicircles, and equilateral triangles. Geometry Trace is used to help students get a “3D” visual of the volume under consideration.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will graphically and numerically explore Riemann sums and develop an understanding of summation notation for adding these rectangles.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will graphically and numerically explore Riemann sums and develop an understanding of summation notation for adding these rectangles.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will graphically discover how to find the average value of a function. This exploration uses animation and graphical observations to develop understanding. Self-check questions engage students and help deepen understanding. Multiple-choice exam-like questions are also included to apply what has been learned. Additionally, students will review concepts like average rate of change and using the Trapezoid Rule to find the definite integral when given only data.
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Texas Instruments, Inc.
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ResourceSpotlight
Students numerically and graphically investigate integrals using area accumulation. Animation and graphics develop understanding. Self-check questions deepen students' understanding. Geometry Trace shows the family of functions produced by changing the value of a in the integral of f(x) from a to x. The kinematic relationships for integration are used with a piecewise function and actual data. Students predict and sketch the graph with the initial conditions.
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Texas Instruments, Inc.
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ResourceSpotlight
Students will explore Riemann sums to approximate the area under the graph of y = x2 on the interval [0, 1]. They will use the Rectangle tool to draw left-endpoint, right-endpoint, and midpoint approximating rectangles. Students will write area formulas in expanded form and summation notation and analyze how their approximations compare to the exact area. Students will use these findings to understand that an infinite number of approximating rectangles will yield the exact area under a curve.
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Texas Instruments, Inc.
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ResourceSpotlight
In this activity, students will use integration by parts to integrate ln x. In the homework/extension problems, they will use a similar process to integrate tan-1x. Self-check questions engage students and help deepen understanding. Multiple-choice exam-like questions are also included to apply what was learned. Additionally, students will review integration using substitution.
|
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Texas Instruments, Inc.
|
|
|
ResourceSpotlight
In this activity, students will graphically discover how to find the average value of a function. This exploration uses animation and graphical observations to develop understanding. Self-check questions engage students and help deepen understanding. Multiple-choice exam-like questions are also included to apply what has been learned. Additionally, students will review concepts like average rate of change and using the Trapezoid Rule to find the definite integral when given only data.
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Texas Instruments, Inc.
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