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Question
Solve the following :
Find the area of the region bounded by the curve y = x2 and the line y = 10.
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Solution
Given equation of the curve is
y = x2
∴ x = `sqrt(y)` ...[∵ In first quadrant, x> 0]
Required area = area of the region ORQPO
= 2 (area of the region ORQO)
= `2 int_0^10x*dy`
= `2int_0^10 y^(1/2)*dy`
= `2[y^(3/2)/(3/2)]_0^10`
= `(4)/(3)[(10)^(3/2) - 0]`
= `(4)/(3)(10sqrt(10))`
= `(40sqrt(10))/(3)"sq.units"`.
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