Question:
find the area of the region bounded by x square = 4y, y=2, y=4, and the y-axis in the first quadrant.
Answer:
From the figure,
The area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant is the area of ABCD
Now area of ABCD = ∫2 4 x dy
= ∫2 4 √y dy
= 2[y3/2 /(3/2) 2]4
= (4/3)*[43/2 - 23/2]
= (4/3)*[8 - 2√2]
= (32 - 8√2)/3
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