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Question
Using integration, find the area of the region bounded between the line x = 4 and the parabola y2 = 16x.
Solution
The shaded region OACO is the region bounded by the parabola y2 = 16x and the line x = 4.
The area OACO is symmetrical about X-axis.
Area of OACO = 2(Area of OAB)
= `2 int_0^4 "y dx"`
= `2 int_0^4 4sqrt"x" "dx"`
= `8 xx 2/3 ["x"^(3//2)]_0^4`
= `16/3 (4)^(3//2)`
= `16/3 xx 8`
= `128/3`
So, the required area is `128/3` sq. units.
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