Mass Given Density Function and Area

[Grace Pseudonym]

Homework Statement

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.

Homework Equations

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.

 

[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?

 

[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

 

[vela]

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?

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.

 

[Grace Pseudonym]

UPDATE NO. 2:

I figured it out.

 

[Grace Pseudonym]

Thank you everyone for your help :)

 

[vela]

You stumbled onto the correct answer, but your work isn't correct.