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Question
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
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Solution
Given equation of the parabola is x2 = 36y
∴ x = `6sqrt(y)` .....[∵ In first quadrant x > 0]
∴ Required area = area of the region ABCDEFA
= 2(area of the region BCDEB)
= `2 int_1^4 x "d"y`
= `2 int_1^4 6sqrt(y) "d"y`
= `12 int_1^4 sqrt(y) "d"y`
= `12[(y^(3/2))/(3/2)]_1^4`
= `8[(4)^(3/2) - (1)^(3/2)]`
= 8(8 –1)
= 8(7)
= 56 sq. units
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