Areas
David Brown
6 min read
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Study Guide Overview
This guide covers calculating areas using multiple integrals and absolute values. It addresses areas partly above/below the x-axis and between two curves. Key concepts include splitting integrals at intersection points and using the absolute value of the function or the difference of functions. The guide also includes practice questions, a glossary, exam strategies, and real-world applications.
Introduction In calculus, definite integrals are used to find the area under a curve. However, calculating areas can become complex when the region of interest lies partly above and partly below the x-axis or between multiple curves. This guide will help you understand how to handle these situations using multiple integrals and absolute values.
#Finding Areas Using Multiple Integrals
#Areas Partly Above and Below the x-axis
When a region between a curve and the x-axis lies partly above and partly below the x-axis, it is essential to calculate areas separately for each part.
To find the total area, integrate the function for each segment and sum the absolute values of the integrals where the function is below the x-axis.
#Formula:
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