COMEDK · Maths · 28. Indefinite Integration
The area of the region bounded by the ellipse \(\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\) is
- A \(\pi a b^2\) sq units
- B \(\pi a b\) sq units
- C \(\pi^2 a b\) sq units
- D \(\pi a^2 b\) sq units
Answer & Solution
Correct Answer
(B) \(\pi a b\) sq units
Step-by-step Solution
Detailed explanation
The equation of the ellipse is \(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\). Solving for \(y\), we get \(y = \pm \dfrac{b}{a} \sqrt{a^2 - x^2}\). The area \(A\) of the ellipse is given by \(4 \times \int_{0}^{a} y \, dx = 4 \int_{0}^{a} \dfrac{b}{a} \sqrt{a^2 - x^2} \, dx\).…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If in a \(\triangle A B C, \angle C=\frac{\pi}{2}\), then \(\tan ^{-1}\left(\frac{a}{b+c}\right)+\tan ^{-1}\left(\frac{b}{c+a}\right)=\)COMEDK 2017 Hard
- A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?COMEDK 2024 Medium
- The solution of \(dy = \cos x (2 - y \ \text{cosec} \ x) dx\) where \(y = \sqrt{2}\) when \(x = \dfrac{\pi}{4}\) isCOMEDK 2026 Medium
- A unit vector perpendicular to both the vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}\) and \(\hat{\mathbf{j}}+\hat{\mathbf{k}}\) isCOMEDK 2019 Medium
- The point of intersection of the lines \(\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}\) and \(\dfrac{x-4}{5}=\dfrac{y-1}{2}=z\) isCOMEDK 2021 Easy
- \(\int \dfrac{d x}{x \sqrt{4 x^2-9}}=\)COMEDK 2025 Medium
More PYQs from COMEDK
- In tetrahedral permanganate ion \(\pi\)-bonding type between metal and oxygen isCOMEDK 2015 Medium
- In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio between bright and dark fringes is 3 . Then, the value of the ratio of the amplitudes of the wave that arrive there isCOMEDK 2023 Medium
-
Two long parallel conductors X and Y are placed vertically at a distance d apart. Conductor X carries a current I upwards and conductor Y carries a current 2I downwards. A third long conductor Z is placed parallel to both X and Y and between X and Y. If Z carries a current I upwards and is at a distance \(x\) from conductor X, then:COMEDK 2026 Medium - A number \(\mathrm{n}\) is chosen at random from \(s=\{1,2,3, \ldots, 50\}\). Let \(\mathrm{A}=\{n \in s: n\) is a square \(\}\), \(\mathrm{B}=\{n \in s: n\) is a prime \(\}\) and \(\mathrm{C}=\{n \in s: n\) is a square \(\}\). Then, correct order of their probabilities isCOMEDK 2023 Hard
- Which of the following compound cannot be prepared by Williamson's synthesis?COMEDK 2024 Medium
- A wire of uniform cross section and resistance 4 ohms is bent in the shape of square ABCD. Point A is connected to a point \(\mathrm{P}\) on DC by a wire AP of resistance \(1 \mathrm{ohm}\). When a potential difference is applied between \(\mathrm{A}\) and \(\mathrm{C}\), the points \(\mathrm{B}\) and \(\mathrm{P}\) are seen to be in same potential. What is the resistance of part \(\mathrm{DP}\) ?
COMEDK 2024 Medium