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प्रश्न
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
विकल्प
63 sq. units
`(3)/(56)"sq. units"`
`(56)/(3)"sq. units"`
`(63)/(7)"sq. units"`
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उत्तर
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is `bbunderline((56)/(3)"sq. units")`.
Explanation:
Required area = `int_1^4x*dy`
= `int_1^4 4sqrt(y)*dy`
= `4[y^(3/2)/(3/2)]_1^4`
= `(8)/(3)[(4)^(3/2) - (1)^(3/2)]`
= `(8)/(3)(8 - 1)`
= `(56)/(3)"sq.units"`.
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