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Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5 - Mathematics and Statistics

Sum

Find the area of the region bounded by the following curves, the X-axis and the given lines:  y = x4, x = 1, x = 5

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Solution

Let A be the required area.
Consider the equation y = x4.

∴ A = `int_1^5 y*dx`

= `int_1^5 x^4*dx`

= `[(x^5)/5]_1^5`

= `(1)/(5)[x^5]_1^5`

= `(1)/(5)[(5)^5 - (1)^5]`

= `(1)/(5)(3125 - 1)`

∴ A = `(3124)/(5)`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 1.1 | Page 157
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