OEF double integrals --- Introduction ---

This module actually contains 4 exercises on double integrals.

Double Integrals I

For the domain D in the drawing where the equation of the green line is y= pour le x le , one has

intint D f(x,y) dx dy =int leftpar2 int f(x,y)dyrightpar2 dx

xrange , yrange , linewidth=2 plot green, segment ,,,, blue segment ,,,, blue segment ,,,, blue fill ,, skyblue text black,,0,giant, text black,,0,giant, linewidth 1 vline 0,, black hline ,0, black hline , , black text black,,,giant, y= parallel ,,,, 0,1, 20, grey parallel ,,,, 1,0, 20, grey arrow 0,, 0,,10,black arrow ,0, ,0 ,10,black

Double Integrals II

Let , , , , , be points in the plane and the domain bounded by the polygonal line (see drawing). One can write the double integral intint D f(x,y) dx dy as

.

What are the missing bounds ?

xrange , yrange , linewidth=2 fpoly skyblue,,,,,,, poly blue,,,,,,, text black,,giant,A text black,,giant,B text black,,giant,C text black,,giant,D text black,,giant,E text black,,giant,F linewidth 1 vline 0,0, black hline 0,0, black parallel ,,,, 0,1, 20, grey parallel ,,,, 1,0, 20, grey arrow 0,, 0,,10,black arrow ,0, ,0 ,10,black

Double Integrals III

Let A=(,), B=(,), C=(,), D=(,), E=(,), F=(,) be points of the plane and the domain bounded by the polygonal line (see drawing). One can write the double integral intint D f(x,y) dx dy as

. What are the missing bounds ?

xrange , yrange , linewidth=2 fpoly skyblue,,,,,,, poly blue,,,,,,, text black,,giant,A text black,,giant,B text black,,giant,C text black,,giant,D text black,,giant,E text black,,giant,F linewidth 1 hline 0,0, black hline 0,0 , black parallel ,,,, 0,1, 20, grey parallel ,,,, 1,0, 20, grey arrow 0,, 0,,10,black arrow ,0, ,0 ,10,black

Double Integrals IV

Let A=(), B=(), C=(), D=(), E=(), F=() be points in the plane and the domain bounded by the polygonal line (see drawing). One can write the double integral intint D f(x,y) dx dy on the form 1

.

or on the form 2

with reals. Which one do you choose (1 ou 2)? What are the bounds ?		 xrange , yrange , linewidth=2 fpoly skyblue,,,,,,, poly blue,,,,,,, text black,,giant,A text black,,giant,B text black,,giant,C text black,,giant,D text black,,giant,E text black,,giant,F linewidth 1 hline 0,0, black hline 0,0 , black parallel ,,,, 0,1, 20, grey parallel ,,,, 1,0, 20, grey arrow 0,, 0,,10,black arrow ,0, ,0 ,10,black
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