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The area enclosed between the parabola y2 = 4x and line y = 2x is ______. - Mathematics and Statistics

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Question

The area enclosed between the parabola y2 = 4x and line y = 2x is ______.

Options

  • `(2)/(3)` sq units

  • `(1)/(3)` sq unit

  • `(1)/(4)` sq unit

  • `(3)/(4)` sq unit

MCQ
Fill in the Blanks
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Solution

The area enclosed between the parabola y2 = 4x and line y = 2x is `bbunderline((1)/(3) "sq unit")`.

Explanation:

Area = `int_0^1 [2sqrt x - 2x]`

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

= `2(2/3 - 1/2) xx 1`

= `4/3 - 1`

`1/3` sq. units.

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Area Bounded by the Curve, Axis and Line
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Chapter 5: Application of Definite Integration - Miscellaneous Exercise 5 [Page 188]

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Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 12 Maharashtra State Board
Chapter 5 Application of Definite Integration
Miscellaneous Exercise 5 | Q 1.04 | Page 188

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