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Solve the following : Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis. - Mathematics and Statistics

Sum

Solve the following :

Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.

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Solution


Given equation of the curve is x2 = 25y
∴ `5sqrt(y)`      ...[∵ In first quadrant, x > 0]
Required area = area of the region PRSVP
= 2(area of the region QRSTQ)

= `2int_1^4x*dy`

= `2int_1^4 5sqrt(y)*dy`

= `10 int_1^4 y^(1/2)*dy`

= `10[y^(3/2)/(3/2)]_1^4`

= `(20)/(3)[(4)(3/2) - (1)^(3/2)]`

= `(20)/(3)(8 - 1)`

= `(20)/(3)(7)`

= `(140)/(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
Miscellaneous Exercise 7 | Q 4.6 | Page 158
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