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प्रश्न
Find the area of the region bounded by the line y = 2x + 5 and the parabola y = x2 – 2x
उत्तर
First, we find the point of intersection of
y = 2x + 5 and y = x2 – 2x
x2 – 2x = 2x + 5
x2 – 4x – 5 = 0
(x – 5)(x + 1) = 0
x = 5, x = – 1
when x = 5, y = 15
x = – 1, y = 3
(5, 15)(– 1, 3) are intersecting points.
Area required = `int_"a"^"b" (y_"L" -y_"C") "d"x`
= `int_(-1)^5 (2x + 5) "d"x - int_(-1)^5 (x^2 - 2x) "d"x`
= `[(2x^2)/2 + 5x]_(-1)^5 - [x^3/3 - (2x^2)/2]_(-1)^5`
= `[25 + 25 - 1 + 5] - [125/3 - 25 + 1/3 + 1]`
= 54 – 18
= 36
Area required = 36 sq. units
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