Find the area of the region enclosed by the curve y = 2√x, the x-axis and the lines x = 1 and x = 4.
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Find the area of the region enclosed by the curve y = 2√x, the x-axis and the lines x = 1 and x = 4.

[From: ] [author: ] [Date: 12-04-03] [Hit: ]
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A = ∫₁⁴ 2√x dx
A = 2 x^(3/2) * 2/3 |₁⁴
A = 4/3 x^(3/2) |₁⁴
A = 4/3 (4^(3/2) − 1^(3/2))
A = 4/3 (8−1)
A = 28/3

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S (1 to 4) 2 x^(1/2) dx

straight forward integration

= 2 x^(3/2) / (3/2) ] 1 to 4

= 4/3 x^(3/2) ] 1 to 4

= 4/3 (8-1) = 28/3
1
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