1 min readโขjune 8, 2020

Sumi Vora

Once you get the hang of finding the area under one curve,** finding the area between two curves** is pretty simple. Remember from previous units that when you find the area between two curves, you subtract the bottom curve from the top curve. This is the same in polar functions, but instead of subtracting โtop minus bottom,โ youโll subtract **โouter minus inner.โ**ย

If the curves intersect, then you may have to find the area inside the curves by splitting the region.ย

Since the graphs intersect at ฮธ = 2 we can see that when ฮธ < ฯ/2, r = 4 is on top, and when ฮธ > ฯ/2, r = 4+2sin(2ฮธ) is on top. Based on this information, we can **construct two integrals**:

There is one last thing you need to know about polar functions: arc length. Finding arc length is pretty straightforward, but you do need to have the formula memorized for the exam.ย

Browse Study Guides By Unit

๐Unit 1 โ Limits & Continuity

๐คUnit 2 โ Fundamentals of Differentiation

๐ค๐ฝUnit 3 โ Composite, Implicit, & Inverse Functions

๐Unit 4 โ Contextual Applications of Differentiation

โจUnit 5 โ Analytical Applications of Differentiation

๐ฅUnit 6 โ Integration & Accumulation of Change

๐Unit 7 โ Differential Equations

๐ถUnit 8 โ Applications of Integration

๐ฆUnit 9 โ Parametric Equations, Polar Coordinates, & Vector-Valued Functions (BC Only)

โพUnit 10 โ Infinite Sequences & Series (BC Only)

๐งMultiple Choice Questions (MCQ)

โ๏ธFree Response Questions (FRQ)

๐Big Reviews: Finals & Exam Prep

ยฉ 2023 Fiveable Inc. All rights reserved.