# Area under a curve

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Taught by TheMathDude
• Currently 4.0/5 Stars.
5594 views | 1 rating
Part of video series
Meets NCTM Standards:
Lesson Summary:

This video on "Area under a Curve" teaches the viewer how to interpret and compute integrals, both graphically and mathematically. It explains the concept of the area between two curves, and how to relate it to the algebraic representation as a definite integral. The transcript provides step-by-step instructions on how to solve a few different examples of integration problems using the calculator's integration features.

Lesson Description:

Be able to interpret what the integral or area below a given business function (e.g. marginal cost) represents (e.g. total cost). Be able to compute that integral (area) given the function and limits. Be able to relate the area between two curves (functions) on a Cartesian graph to the algebraic representation as a definite integral of a difference of those two functions.

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Additional Resources:
• Computing Technology for Math Excellence - Devoted to the standards movement and integrating technology into teaching and learning and in K-12 mathematics and calculus. Find software and sites for teaching and learning math with technology. Accessibility resources are included.
Questions answered by this video:
• How do you find the area under a curve using a TI graphing calculator?
• How do you find definite integrals using a TI graphing calculator?
• What is the integral of x/(2x^2 - 5) dx between 2 and 3?
• How can you use the Equation Solver on a TI graphing calculator to find an integral?
• How can you find the area of the region bounded by the curve y = square root of x, the x-axis, and the lines x = 0 and x = 4?
• If the marginal revenue of the xth box of zip disks sold is 100e^(-0.001x) dollars, what is the revenue generated by selling items 101 through 1000?
• What happens when you take a definite integral of the derivative of a function?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson shows the process of finding the definite integral of a function on a TI graphing calculator. All steps involved in putting the functions into the calculator and finding the area within a region are shown and explained. This is a great tutorial on finding integrals on a graphing calculator.