1 min readβ’june 18, 2024

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**.Β

Letβs 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 youβre 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.Β

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.

Browse Study Guides By Unit

πUnit 1 β Limits & Continuity

π€Unit 2 β Fundamentals of Differentiation

π€π½Unit 3 β Composite, Implicit, & Inverse Functions

πUnit 4 β Contextual Applications of Differentiation

β¨Unit 5 β Analytical Applications of Differentiation

π₯Unit 6 β Integration & Accumulation of Change

πUnit 7 β Differential Equations

πΆUnit 8 β Applications of Integration

π¦Unit 9 β Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

βΎUnit 10 β Infinite Sequences & Series (BC Only)

πStudy Tools

π€Exam Skills

Β© 2024 Fiveable Inc. All rights reserved.