- #1

apples

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What I'm facing problems with is that when I find the area, I don't know how to find the limits.

## Homework Statement

Sample problem:

Find the area of the region in the plane enclosed by the cardioid r=4+(4sinθ)

## Homework Equations

b

A = ∫ (1/2)(r^2) dθ

a

## The Attempt at a Solution

Graphing the curve is no biggie, I use my calculator. The problem is when I use the equation to find the Area, I don't know what the interval is I don't know 'b' and 'a' are.

I have a calculus book, an AP calculus book, and a pre-calculus book. None of the books tell you how to find the interval. In their solved questions, they tell you that in the solution. The problem I wrote above is an example also.

They tell you the interval is (for the q above) 0 to 2π(pi)

but how do i know that what about other questions.

Another example:

Find the area inside the smaller loop of the limacon r=1+(2cosθ)

Here they say the limits are (2π(pi))/(3) to (4π(pi))/3

The exact explanation to this in the book is:

(for first question) "Because r swoops out the region as θ goes from 0 to 2π(pi), these are our limits of integration.

(For 2nd q) Because in the inner loop, r sweeps out the region as θ goes from (2π(pi))/(3) to (4π(pi))/3, these are our limits of integration.

But why!? What does r swoops mean. How do I know the limits!?

please help!