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Question
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
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Solution
The given equation of the curve is x2 = 25y.
∴ `5sqrt(y)` ...(∵ In first quadrant, x > 0)
Required area = `int_1^4x.dy`
∴ A = `int_1^4 5sqrt(y).dy`
∴ A = `5int_1^4 y^(1/2).dy`
∴ A = `5[(y^(3/2))/(3/2)]_1^4`
∴ A = `5 × 2/3 [4^(3/2) - 1]`
∴ A = `10/3 [(2^2)^(3/2) - 1]`
∴ A = `10/3 [8 - 1]`
∴ A = `10/3 × 7`
∴ A = `70/3` sq. units
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