Final answer:
The area of the region bounded by x = 0, y = 2x + 1, and y = -2x + 5 is 8 square units.
Step-by-step explanation:
To determine the area of the region bounded by x = 0, y = 2x + 1, and y = -2x + 5, we need to find the points of intersection between the curves. The area of the region bounded by x = 0, y = 2x + 1, and y = -2x + 5 is 8 square units.
Setting 2x + 1 = -2x + 5, we get 4x = 4, which gives x = 1. Substituting x = 1 into any of the equations, we find y = 2(1) + 1 = 3. So the points of intersection are (1, 3).
To find the area between the curves, we integrate from x = 0 to x = 1, using the formulas for the curves: y = 2x + 1 and y = -2x + 5. The area is given by the integral of (2x + 1) - (-2x + 5) dx, which simplifies to the integral of 4x + 4 dx. Solving this integral gives us the area as 8 square units.