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Find the area of the region bounded by the following curves, the X-axis and the given lines: y = 2 – x2, x = – 1, x = 1 - Mathematics and Statistics

Sum

Find the area of the region bounded by the following curves, the X-axis and the given lines: y = 2 – x2, x = – 1, x = 1

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Solution

Let A be the required area.
Consider the equation y = 2 – x2.

∴ A = `int_(-1)^(1) y*dx`

= `int_(-4)^(1)(2 - x^2)*dx`

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

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

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

= `(5)/(3) - ((-5)/3)`

∴ A = `(10)/(3)`sq. units.

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 7 Applications of Definite Integration
Exercise 7.1 | Q 1.7 | Page 157
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