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Find the area, in square units, of the part of the first quadrant enclosed by the parabola y = 9x² and the lines x = 0, y = 1, and y = 4.
- 7/9
- 14/3
- 7/3
- 14/9
Correct answer: 14/9
Solution
The area is determined by integrating the difference between the upper line (y = 4) and the parabola (y = 9x²) from the intersection points of the parabola with y = 1 and y = 4. This results in a calculated area of 14/9 square units, which represents the region in the first quadrant bounded by the specified lines and the parabola.
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