# Finding area between two curves Polar Coordinates

• PsychonautQQ
In summary, the question asks to find the area inside a circle with radius 3sinθ and outside a carotid with radius 1 + sinθ. The solution involves finding the limits of integration, graphing the two shapes and finding their points of intersection, and using the formula for polar area to find the integral of (3sinθ - (1+sinθ)). Wolfram Alpha can be used to check the final answer.

## Homework Statement

Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ

## The Attempt at a Solution

Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost

PsychonautQQ said:

## Homework Statement

Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ

## The Attempt at a Solution

Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost

Yes, that all seems reasonable. Just compute your integral and you're done.

• 1 person
I got 1.369705. Is there any online integral doer I can use to check my work?

PsychonautQQ said:
I got 1.369705. Is there any online integral doer I can use to check my work?

Yes, that's the correct answer. Wolfram alpha is good for checking your work afterwards.

• 1 person
PsychonautQQ said:

## Homework Statement

Find the area inside the circle r = 3sinθ and outside the carotid r = 1 + sinθ

## The Attempt at a Solution

Alright so I graphed it and found that they intersect at ∏/6 and 5∏/6.
I can't think of a good way to approach the problem. The carotid has some of it's area beneath the x-axis otherwise I would take the area of the 3sinθ - the area of the other one. Will it work if set the limits of integration to pi/6 and 5pi/6 and take the integral of (3sinθ - (1+sinθ)? I'm a bit lost

NO. That's the wrong integrand. Look up the formula for polar area.