Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4 - Mathematics and Statistics

Sum

Find the area of the region bounded by the following curves, X-axis and the given lines: y2 = 16x, x = 0, x = 4

Solution

The required area consists of two bounded regions A1 and A2 which are equal in areas.
For y2 = x, y = sqrt(x)
Required area = A1 + A2 = 2A1

= 2int_0^4 y*dx,  "where"  y = sqrt(x)

= 2int_0^4 sqrt(x)*dx

= 2[(x^(3/2))/(3/2)]_0^4

= 2[2/3(4)^(3/2) - 0]

= 2[2/3(2^2)^(3/2)]

= (128)/(3) "sq units".

Concept: Area Bounded by the Curve, Axis and Line
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 5 Application of Definite Integration
Exercise 5.1 | Q 1.7 | Page 187