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Question
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
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Solution
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is `underlinebb(28/3)` sq. units.
Required area = `2int_1^4y*dx`
= `2int_1^4 2sqrt(x)*dx`
= `2[x^(3/2)/(3/2)]_1^4`
= `2[(2x^(3/2))/(3)]_1^4`
Substituting the values we get
= `2 = ((2(4)^(3/2))/3 - (2(1)^(3/2))/3)`
= `4 (8/3 - 1/3)`
= `4 (7/3)`
= `28/3` sq. units.
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