Answer:
Area = 8
Step-by-step explanation:
A skecth is given in the attached file, there are two extra lines used to calculate the area with simple geometry:
We must use a double integral to obtain the area:
[tex]\int\limits^2_0 {\int\limits^b_a \, dy } \, dx[/tex]
Where
b stands for y=2x+1
a stands for y=-x
Carring out the integrals we find the area:
[tex]\int\limits^2_0 {(2x+1 - (-x))} \, dx = \int\limits^2_0 {3x+1} \, dx = (3x^{2}/2+x) \left \{ {{2} \atop {0}} \right.\\ A =( 3*2^{2}/2) + 2 =8[/tex]
Geometrically we can divide the area bounded by this lines as two triangles and a rectangle from the figure and the intersection of these lines we kno that the three figures have a base of 2. The heigth of the rectangle is 1 and for the triangles we have 4 for the upper triangle and 2 for the lower.
Therefore:
[tex]A = A_{upperT}+ A_{rect}+ A_{lowerT}[/tex]
and
[tex]A_{upperT}=2*4/2=4\\A_{rect}=2*1=2\\ A_{lowerT}=2*2/2=2[/tex]
Summing the four areas we have:
A=8
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