TS EAMCET · Maths · Area Under Curves
The area (in sq. units) of the portion lying above the \(X\)-axis and enclosed between the curves \(y^2=2 a x-x^2\) and \(y^2=a x\) is
- A \(a^2\left(\frac{-\pi}{2}+\frac{2}{3}\right)\)
- B \(a^2\left(\frac{2}{3}-\frac{\pi}{4}\right)\)
- C \(a^2\left(\frac{\pi}{4}-\frac{2}{3}\right)\)
- D \(a^2\left(\frac{\pi}{4}+\frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(a^2\left(\frac{\pi}{4}-\frac{2}{3}\right)\)
Step-by-step Solution
Detailed explanation
Equation of given curves \(x^2+y^2-2 a x=0\) and \(y^2=a x\) \(\because\) Area of the portion lying above the \(X\)-axis and enclosed between the given curves, from the diagram is \(\int_0^a\left(\sqrt{2 a x-x^2}-\sqrt{a x}\right) d x\)…
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
- The solution set of \((5+4 \cos \theta)(2 \cos \theta+1)=0\) in the interval \([0,2 \pi]\), is :TS EAMCET 2003 Medium
- \(p\) points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points isTS EAMCET 2009 Hard
- The normal to a circle \(S=0\) at \(P(1,3)\) is \(x+2 y=7\) and it has another normal at \(Q(3,5)\) which is the polar of the point \(A\left(7,-\frac{1}{2}\right)\) with respect to the circle \(x^2+y^2-4 x+6 y-12=0\). Then, the equation of the circle \(S=0\) isTS EAMCET 2018 Medium
- If is a point on the hyperbola , where is the parameter in its parametric form, thenTS EAMCET 2022 Easy
- 4-digit numbers are formed using the digits \(4,5,6,7,8,9\) allowing repetition of the given digits. If a number is chosen at random from those numbers thus formed, then the probability that it is exactly divisible by 3 isTS EAMCET 2020 Easy
- If \(1+2 i\) is a root of the equation \(x^4-3 x^3+8 x^2-7 x+5=0\), then sum of the squares of the other roots isTS EAMCET 2025 Hard
More PYQs from TS EAMCET
- If thenTS EAMCET 2021 Easy
- \(\mathbf{a}=\mathbf{i}+\mathbf{j}-2 \mathbf{k} \Rightarrow \sum\{(\mathbf{a} \times \mathbf{i}) \times \mathbf{j}\}^2\) is equal toTS EAMCET 2012 Easy
- Observe the following lists
Then the correct match for List I from List II is A B C DTS EAMCET 2005 Medium - A coil having 2000 turns is wound tightly in the form of a spiral with inner and outer radii \(1 \mathrm{~cm}\) and \(3 \mathrm{~cm}\), respectively. When a current \(\frac{1}{\pi} \mathrm{mA}\) passes through the coil, then the magnetic field at the centre is calculated be \(K \ln 3 \times 10^{-6} \mathrm{~T}\). The value of \(K\) isTS EAMCET 2021 Hard
- When \(n-p-n\) transistor is used as an amplifier :TS EAMCET 2003 Easy
- If the slope of the tangent of the circle \(S \equiv x^2+y^2-13=0\) at \((2,3)\) is \(m\), then the point \(\left(m, \frac{-1}{m}\right)\) isTS EAMCET 2017 Medium