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Vector Algebra

Question

Find the area of the region lying in the first quadrant and bounded by x² = y - 3, y = 4, y = 6 and the y-axis in the first quadrant.

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Solution

The equation of curve is x² = y - 3. which is an upward parabola whose vertex is (0,3).
Lines are y = 4, y = 6
Required area = Area ABCD

equals space integral subscript 4 superscript 6 straight x space dy space equals space integral subscript 4 superscript 6 square root of straight y minus 3 end root space dy

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