Home
Class 12
MATHS
Find the area of the region bounded by ...

Find the area of the region bounded by the ellipse `(x^2)/(16)+(y^2)/9=1`.

Text Solution

Verified by Experts

Given curve is an ellipse which is symmetric about X-axis both, as shown in the figure.

` :. ` Area bounded by ellipse
`=4xx` (area of shaded region in first quadrant)
`=4 xx int_(0)^(4)ydx`
`=4 int_(0)^(4)(3)/(4)sqrt(16-x^(2))dx`
`=3*int_(0)^(4)sqrt(4^(2)-x^(2))dx`
`=3[(x)/(2)sqrt(4^(2)-x^(2))+(4^(2))/(2)"sin"^(-1)((x)/(4))]_(0)^(4)`
`=3[2sqrt(16-16)+8"sin"^(-1)(1)-0-8sin^(-1)(0)]`
`=3[0+8"sin"^(-1)(1)-0]`
`=3xx8xx((pi)/(2))=12pi` sq. units.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Exercise 8.2|7 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Exercise 8 C Questions For Competitive Examinations|10 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|24 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Find the area of the region bounded by the ellipse (x^(2))/(4)+(y^(2))/(9)=1

Find the area of the region bounded by the ellipse (x ^(2))/(4) + (y ^(2))/(9) =1.

Find the area of the region bounded by the ellipse (x^(2))/(9)+(y^(2))/(4)=1 in fourth quadrant.

Find the area of the region bounded by the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

Using definite integration,find the area of the smaller region bounded by the ellipse 9x^(2)+16y^(2)=144 and x=2

Find the area of the smaller region bounded by the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and the line (x)/(3)+(y)/(2)=1

Find the area of the smaller region bounded by the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and the line (x)/(3)+(y)/(2)=1

The area of the region bounded by the ellipse (x^(2))/25+y^(2)/16=1 is

The area of the region bounded by the ellipse (x^(2))/25+y^(2)/16=1 is