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Find the area of the region included between y2 = 9x and y = x - Mathematics

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Question

Find the area of the region included between y2 = 9x and y = x

Sum
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Solution


Given that, y2 = 9x  .....(i)

And y = x  .....(ii)

Solving equation. (i) and (ii)

We have x2 = 9x

⇒ x2 – 9x = 0

x(x – 9) = 0

∴ x = 0, 9

Required area = `int_0^9 sqrt(9x)  "d"x - int_0^9 x  "d"x`

= `3int_0^9 sqrt(x)  "d"x - int_0^9 x  "d"x`

= `3 * 2/3 [x^(3/2)]_0^9 - 1/2 [x^2]_0^9`

= `2[(9)^(3/2) - 0] - 1/2 [(9)^2 - 0]`

= `2(27) - 1/2 (81)`

= `54 - 81/2`

= `(108 - 81)/2`

= `27/2` sq.units

Hence, the required area = `27/2` sq.units

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Chapter 8: Application Of Integrals - Exercise [Page 176]

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NCERT Exemplar Mathematics [English] Class 12
Chapter 8 Application Of Integrals
Exercise | Q 5 | Page 176

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