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Question
Find the area of the region bounded by the curves y2 = 9x, y = 3x
Solution
We have, y2 = 9x, y = 3x
Solving the two equations,
We have (3x)2 = 9x
⇒ 9x2 – 9x = 0
⇒ 9x(x – 1) = 0
∴ x = 0, 1
Area of the shaded region
= ar (region OAB) – ar (ΔOAB)
= `- int_0^1 y_1 * "d"x`
= `int_0^1 sqrt(9x) "d"x - int_0^1 3x "d"x`
= `3 int_0^1 sqrt(x) "d"x - 3 int_0^1 x "d"x`
= `3 xx 2/3 [x^(3/2)]_0^1 - 3[x^2/2]_0^1`
= `2[(1)^(3/2) - 0] - 3/2 [(1)^2 - 0]`
= `2(1) - 3/2 (1)`
= `2 - 3/2`
= `1/2` sq.units
Hence, the required area = `1/2` sq.units
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