Find the area of the bounded region

[tix24]

Hi guys I am very new here this is my second post. (sorry in advance i don't know how to use the functions of the site fully yet)

i think this is the correct method to follow, some feedback or hints would be great thanks in advance!

1. Homework Statement
Find the area bounded by where 0≤theta≤pie

r=1/√(1+theta)

Homework Equations

The Attempt at a Solution

(∫ dtheta ) (∫rdr)

bounds of integration ∫dtheta from o to pie

bounds of integration ∫rdr from 0 to r=1/√(1+theta)

 

[Orodruin]

Good start, now you just need to perform the integrals.

 

[tix24]

Good start, now you just need to perform the integrals.

im more worried about the method, we are suppose to use double integrals, but i got confused over the graph of this function. I checked it in wolfram and it was looping in it self, that is why i don't know if the integrals are set up correctly or not.
any tips regarding the set up of the integral it self?

 

[Orodruin]

You already did. Naturally, if you give the radius as a function of an angle, you will get some sort of loop or spiral unless you bound the argument. In your case it is bounded to be between 0 and π.

 

[tix24]

You already did. Naturally, if you give the radius as a function of an angle, you will get some sort of loop or spiral unless you bound the argument. In your case it is bounded to be between 0 and π.

thank you very much, it was very helpful of you