Setting up a double integral over two regions

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Mdhiggenz
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Homework Statement



MathGV screenshot of a plotted region bounded by the lines y = x, x = 1 and y = 0 with hatched shading, plus the integral of cos(x^2) over the region, with labelled horizontal line y = sqrt(pi).




Homework Equations





The Attempt at a Solution



The question is in the picture, the new integral I got was

R1:0≤y≤x

R2:0≤x≤1

However the answer is
R1: is inner integral R2: is outer integral

I drew a graph showing my thought process.

R1:0≤y≤x

R2:0≤x≤√∏
 
The double integral says y goes up to root pi. What does the inner integral look like when y is 1.5, say?