Sketch these four lines y = 2x+1, y =-x, and x = 0 and x = 2. then use integrals to find the area of the region bounded by these lines. finally, check your answer by computing this area using simple geometry.

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:

Where

b stands for y=2x+1

a stands for y=-x

Carring out the integrals we find the area:

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:

and

Summing the four areas we have:

A=8

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step-by-step explanation: