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The area of the region enclosed by the graph of y 2 x2 1 and the line y 2 x 5 is what?
Ganderton
∣∣2−1 . -6 + 15 = 9 To calculate the area between the curves y = 2 x2 + 1 and y = 2 x + 5, we must evaluate the integral ∫ab(2x+5)−(2x2+1)dx . To determine which values to use for a and b as the limits of the integral, we calculate the x values where the two curves intersect. Solve 2 x2 + 1 = 2 x + 5 by factoring to get x = 2 and x = -1. Set a = -1, b = 2. The enclosed area, A , is therefore given by the equation A=∫2−1(2x+5)−(2x2+1)dx=∫2−1−2x2+2x+2x+4 dx=[−2x33+x2+4x]
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