You need to use the application "Mathematica" to solve and display the solutions of these problems. I Have attached the region that i need to use too

DOUBLE INTEGRALS You are assigned an individual region R and a function of 2 variables f(x,y). Depending on your lab group, find your region R and your function f(x,y) in the following PDF file: LAB01 Wednesdays - Question 3 DATA.pdf, or LABO2 Tuesdays - Question 3 DATA.pdf, or LAB03 Thursdays - Question 3 DATA.pdf. The region R=R, UR2 is the union of the following two subregions: subregion R, which is the triangle ABC, and subregion R2 which is the region bounded by the parabola passing through A, C and D. Notes. AC is a horizontal line. TASKS (a) Find the equation of lines AB, BC and the parabola ADC. Write them on the table below: Line AB: y = f1(x) = Line BC: y = f2(x) = Parabola ADC: y=f3(x) = (b) (This part must obviously completed by hands) (i) Describe R1 by using horizontal cross-sections: (ii) Describe R, by using vertical cross-sections: (iii) Describe R2 by using vertical cross-sections: (iv) Describe R2 by using horizontal cross-sections (harder): (c) Using Mathematica, give the exact value of the double integral Sf f(x,y)da | by using the following descriptions: (i) both R1 and R2 as vertically simple regions. (ii) R1 as a horizontally simple region and R2 as a vertically simple region. (iii) R1 as a vertically simple region and R2 a horizontally simple region. (iv) both R, and R, as horizontally simple regions. (d) Plot the region R by using Mathematica. It should look like this: A Note. This is my region. Please sketch yours. Hints. Define functions Fabove (x) for the curve MN above the x-axis and Fbelow(x) for the curve MN below the x-axis. These two functions should be defined by cases (i.e. piecewise functions). To define a piecewise function in Mathematica, for example, to define the function: -3x 10, if x