# Fill in the blank : Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______. - Mathematics and Statistics

Fill in the Blanks

Fill in the blank :

Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.

#### 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".

#### Notes

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".

Concept: Area Under Simple Curves
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 7 Applications of Definite Integration
Miscellaneous Exercise 7 | Q 2.1 | Page 158