# Mass Given Density Function and Area

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1. Mar 26, 2016

### Grace Pseudonym

1. The problem statement, all variables and given/known data

A quarter disc of radius 3 cm lies in the first quadrant. The areal density is (1.2 g/cm3)x + (0.7 g/cm3)y. Determine the mass of this object.

2. Relevant equations

3. The attempt at a solution

For my bounds:
x: 0 to 3
y: 0 to Sqrt[3 - x^2]

When I took this integral I got 2.07846 + 5.87878 I, which is obviously an imaginary number. Any idea how to get a real number? I'm not sure where I'm going wrong-- I thought this was simple calculus 2.

2. Mar 26, 2016

### Grace Pseudonym

UPDATE: I have converted to polar coordinates, giving density = 1.2 r Cos[theta]+ 0.7 r Sin[theta]. Then I solved the following integral:

This gave me 8.55 g which was incorrect. Where am I going wrong?

3. Mar 26, 2016

### Nono713

Your bound for y is wrong, draw a diagram with your bounds (e.g. y as a function of x) and you'll see that's not the bounds of a circle quadrant. Hint: the relation is x^2 + y^2 = 3^2

4. Mar 27, 2016

### vela

Staff Emeritus
If you check the units of your expression, you'll see that they don't work out. Your mistake is in the area element for polar coordinates.

5. Mar 27, 2016

### Grace Pseudonym

UPDATE NO. 2:

I figured it out.

6. Mar 27, 2016

### Grace Pseudonym

Thank you everyone for your help :)

7. Mar 27, 2016

### vela

Staff Emeritus