ap calc study guides

๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

8.5 Finding the Area Between Curves Expressed as Functions of y

#areabetweencurves

#integration

โฑ๏ธย ย 1 min read

written by

Anusha Tekumulla

anusha tekumulla


Using the y-axis to Find Area Between Two Curves

This is similar to Topic 8.4 except we are now using curves expressed as functions of y instead of x. If the same function is both the top and the bottom of the slice (like the example below), we must use horizontal slices instead of vertical ones.ย 

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๐Ÿ” Example Problem: Finding the Area Between Two Curves Using Horizontal Slicesย 

Letโ€™s say we want to find the area between the curve x = y^2 and the curve x = y + 6 from y = 0 to y = 3. When you slice up the section horizontally, the right edge of the area youโ€™re trying to find is the curve x = y + 6 and the left edge is the curve x = y^2. Thus, you would integrate (y + 6 - y^2) from 0 to 3 to find the area.ย 

It is important to note that your functions must be expressed in terms of y to use horizontal slicing. Also, your endpoints must be expressed as functions of y. In the example above, the endpoints are y = 0 and y = 3.

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