Double integral on triangle using polar coordinates

[sxyqwerty]

Homework Statement

Let R be the triangle defined by -xtanα≤y≤xtanα and x≤1 where α is an acute angle sketch the triangle and calculate
∫∫_R (x²+y²)dA using polar coordinates
hint: the substitution u=tanθ may help you evaluate the integral

Homework Equations

The Attempt at a Solution

so the triangle has points (0,0) (1, xtanα) (1, -xtanα)
and r=1/cosα=secα
and I am stuck from here i don't know how to find the θ value of the polar coordinate

 

[Orodruin]

The polar angle does not have one value. Like the radial coordinate r, it is an integration variable and you must integrate over it. The question you need to answer first is: What is the integral you need to solve and what are the integration boundaries?

 

[sxyqwerty]

i got ∫∫_R r³drdθ i get that the boundary for r is 0 to secα but I am stuck after this...
i get that the polar angle is supposed to be multiple values (i.e. in a general form like θ or α) but i seriously have no clue on how to approach this further

from the original set of data i get ∫₀¹∫_-xtanα^xtanαx²+y²dA

 

[Orodruin]

i get that the boundary for r is 0 to secα

This is wrong. I suggest you draw the triangle on a piece of paper and try to figure out which limits your integration variables have. Think about what the angles $\alpha$ and $\theta$ represent.