Question
Download Solution PDFFind the area of the region bounded by the parabola x2 = 4y, y = 2 and y= 4 and the y-axis in the first quadrant.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Area under a Curve by Integration: Find the area under this curve is by summing vertically.
In this case, we find the area is the sum of the rectangles, heights x = f(y), and width dy.
If we are given y= f(x), then we need to re-express this as x=f(y) and we need to sum from bottom to top.
Calculation:
Given curve is x2 = 4y
∴ x = 2√y
Here required shaded area of the region lying in the first quadrant bounded by parabola x2 = 4y, and the horizontal lines y = 2 and y = 4.
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