COMEDK · Maths · 31. Area Under Curves
The area of the upper half of the circle whose equation is \((x-1)^2+y^2=1\) is given by
- A \(\dfrac{\pi}{4} \text { sq units }\)
- B \(\int_\limits0^2 \sqrt{2x-x^2} d x \text { sq units }\)
- C \(\int_\limits0^1 \sqrt{2x-x^2} d x \text { sq units }\)
- D \(\int_\limits0^2 \sqrt{2-x^2} d x \text { sq units }\)
Answer & Solution
Correct Answer
(B) \(\int_\limits0^2 \sqrt{2x-x^2} d x \text { sq units }\)
Step-by-step Solution
Detailed explanation
The given equation of the circle is \((x-1)^2 + y^2 = 1\). Expanding the equation, we get \(x^2 - 2x + 1 + y^2 = 1\), which simplifies to \(x^2 + y^2 - 2x = 0\). Solving for \(y\), we have \(y^2 = 2x - x^2\), which gives \(y = \pm \sqrt{2x - x^2}\). The upper half of the circle…
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
- Find the value of \(\lim _{h \rightarrow 0} \dfrac{(a+h)^2 \sin (a+h)-a^2 \sin a}{h}\)COMEDK 2025 Medium
- If \(\vec{a}, \vec{b}, \vec{c}\) are three vectors such that \(a \neq 0\), \(|\vec{a}| = |\vec{c}| = 1, |\vec{b}| = 4\) and \(|\vec{b} \times \vec{c}| = \sqrt{15}\). If \(\vec{b} - 2\vec{c} = \lambda\vec{a}\) then \(\lambda^2\) equals:COMEDK 2025 Medium
- If \(y=\log _{a} x+\log _{x} a+\log _{x} x+\log _{a} a\), then \(\frac{d y}{d x}\) is equal toCOMEDK 2017 Easy
- Evaluate \(i^{2024}+i^{2025}+i^{2026}+i^{2027}\) (where \(i=\sqrt{-1})\)COMEDK 2024 Easy
- In a triangle ABC the coordinate of the vertex A is \((1,2)\). Equations of the median through B and C are respectively \(x+y=5\) and \(x=4\). Then the equation of side \(\mathrm{A B}\) isCOMEDK 2025 Medium
- Let A and B be two subsets of \(\xi = \{1, 2, 3, -------, 44, 45\}\) such that
\(A = \{x: x \text{ is divisible by } 3 \text{ and } 4\}\)
\(B = \{x: x \text{ is a perfect square number}\}\)
Then \(n(B - A)\) equalsCOMEDK 2026 Easy
More PYQs from COMEDK
- An ideal gas heat engine operates in a Carnot's cycle between \(227^{\circ} \mathrm{C}\) and \(127^{\circ} \mathrm{C}\). It absorbs \(6 \times 10^{4}\) J at high temperature. The amount of heat converted into work isCOMEDK 2019 Medium
- The general formula of a cycloalkene isCOMEDK 2020 Easy
- If a class of 175 students the following data shows the number of students opting one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40 . Mathematics and Physics 30 , Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18 . The number of students who have opted Mathematics alone isCOMEDK 2015 Easy
- A solution of \(\mathrm{KCl}(\mathrm{M}=74.5 \mathrm{~g} \mathrm{~mol}^{-1})\) containing \(1.9 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of \(\mathrm{KCl}\) is isotonic with a solution of urea \((\mathrm{M}=60.0 \mathrm{~g} \mathrm{~mol}^{-1}\)) containing \(3 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of urea. The degree of dissociation of \(\mathrm{KCl}\) is:
[Assume both the solutions are kept at same temperature]COMEDK 2024 Medium - The escape velocity of a projectile on the earth's surface is \(11.2 \mathrm{~km} / \mathrm{s}\). A body is projected out with thrice this speed. The speed of the body far away from the earth will beCOMEDK 2022 Easy
- The distance of the point \((3,4)\) from the line \(3 x+2 y+7=0\) measured along the line parallel to \(y-2 x+7=0\) is equal toCOMEDK 2023 Medium