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Question
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
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Solution
The region bounded by the parabola `y^2` = 16x and
the line x = 4 is the area OACO
The area OACO is symmetrical about x-axis
Area of OACO = 2(Area of OAB)
Area of OACO = `2int_0^4y dx`
=`2int_0^4 4sqrtx dx`
=`8[x^(3/2 )/(3/2)]_0^4`
=`16/3[x^(3/2)]_0^4`
=`16/3(8)=128/3`
Therefore, the required area is `128/3`sq. units.
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