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Question
Find the area of region bounded by the line x = 2 and the parabola y2 = 8x
Solution
Here, y2 = 8x and x = 2
y2 = 8(2) = 16
∴ y = ±4
Required area = `2 int_0^2 sqrt(8x) "d"x`
= `2 xx 2sqrt(2) int_0^2 sqrt(x) "d"x`
= `4sqrt(2) xx 2/3 [x^(3/2)]_0^2`
= `(8sqrt(2))/3 [(2)^(3/2)]`
= `(8sqrt(2))/3 xx 2sqrt(2)`
= `32/3` sq.units
Hence, the area of the region = `32/3` sq.units
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