CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
Last updated at August 10, 2026 by Teachoo
![Find the area of the ellipse x^2 + 9y^2 = 36 using integration [Video]](https://cdn.teachoo.com/bb9b8aa1-02ea-4f01-82b6-042682e39fce/slide38.jpg)
Note : This is similar to Ex 8.1, 4 of NCERT – Chapter 8 Class 12 Application of Integration
Check the answer here https:// www.teachoo.com /3328/730/Ex-8.1--4---Find-area-bounded-by-ellipse-x2-16---y2-9--1/category/Ex-8.1/
Transcript
Question 34 (Choice 2) Find the area of the ellipse š„2 + 9š¦2 = 36 using integration Equation of Ellipse is :- š„2 + 9š¦2 = 36 š„^2/36+(9š¦^2)/36=1 š„^2/36+š¦^2/4=1 š„^2/6^2 +š¦^2/2^2 =1 Since Ellipse is symmetric along x and y-axis Area of ellipse = Area of ABCD = 4 Ć [Area Of OBC] = 2 Ć ā«_0^6ā暦.ć šš„ Finding y š„2 + 9š¦2 = 36 9š¦2 = 36 ā š„2 š¦^2=1/9 (36āš„^2 ) Taking square root on both sides y = Ā± ā(1/9 (36āš„^2 ) ) y = Ā± 1/3 ā(36āš„^2 ) Since OBC is above x-axis y will be positive ā“ š=š/š ā(ššāš^š ) Area of ellipse = 4 Ć ā«_š^šāćš.ć š š = 4 Ć ā«_0^6āć 1/3 ā(36āš„^2 )ć šš„ = 4/3 ā«_0^6āā((6)^2āš„^2 ) šš„ It is of form ā(š^2āš„^2 ) šš„=1/2 š„ā(š^2āš„^2 )+š^2/2 ćš ššć^(ā1)ā”ć š„/š+šć Replacing a by 6 we get = 4/3 [š„/2 ā((6)^2āš„^2 )+(6)^2/2 sin^(ā1)ā”ć š„/6ć ]_0^6 = 4/3 [6/2 ā((6)^2ā(6)^2 )+18 ć sinć^(ā1)ā”(6/6)ā0/2 ā((6)^2ā(0)^2 )ā18sin^(ā1) (0/6)] = 4/3 [18 sin^(ā1) (1)] = 4/3 Ć 18 Ćš/2 = 12š square units
