JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region bounded by the curves \(y^2-2 y=-x, x+y=0\) is \(A\), then \(8 A\) is equal to
- A \(38\)
- B \(40\)
- C \(85\)
- D \(36\)
Answer & Solution
Correct Answer
(D) \(36\)
Step-by-step Solution
Detailed explanation
\(y^2-2 y=-x\) \(\Rightarrow y^2-2 y+1=-x+1\) \((y-1)^2=-(x-1)\) \(y=-x\) Points of intersection \(x^2+2 x=-x\) \(x^2+3 x=0\) \(x=0,-3\) \(A=\int \limits_0^3\left(-y^2+2 y+y\right) d y\) \(=\frac{3 y^2}{2}-\left.\frac{y^3}{3}\right|_0 ^3=\frac{9}{2}\) \(8 A=36\)
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
- A possible value of \(\tan \left(\frac{1}{4} \sin ^{-1} \frac{\sqrt{63}}{8}\right)\) is :JEE Mains 2021 Medium
- A six faced die is biased such that \(3 \times P (\) a prime number \()=6 \times P (\) a composite number \()=2 \times P (1)\).Let \(X\) be a random variable that counts the number of times one gets a perfect square on some throws of this die. If the die is thrown twice, then the mean of \(X\) is.JEE Mains 2022 Hard
- \(8-\) digit numbers are formed using the digits \(1, 1, 2, 2, 2, 3, 4, 4.\) The number of such numbers in which the odd digits do no occupy odd places, isJEE Mains 2014 Hard
- In a triangle \(ABC ,\) if \(|\overline{ BC }|=8,|\overline{ CA }|=7,|\overline{ AB }|=10,\) then the projection of the vector \(\overline{ AB }\) on \(\overline{ AC }\) is equal to ....... .JEE Mains 2021 Medium
- Let \(A = \left[ {\begin{array}{*{20}{c}}
2&b&1 \\
b&{{b^2} + 1}&b \\
1&b&2
\end{array}} \right]\) where \(b > 0\). Then the minimum value of \(\frac{{\det \left( A \right)}}{b}\) isJEE Mains 2019 Hard - Let \(y = y(x)\) be the solution of the differential equation \((\tan x)^{1/2}\,dy = (\sec^3 x - (\tan x)^{3/2} y)\,dx\), \(0 < x < \dfrac{\pi}{2}\), \(y\left(\dfrac{\pi}{4}\right) = \dfrac{6\sqrt{2}}{5}\). If \(y\left(\dfrac{\pi}{3}\right) = \dfrac{4}{5}\alpha\), then \(\alpha^4\) equals _______.JEE Mains 2026 Hard
More PYQs from JEE Mains
- The number of matrices \(A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\), where a \(, b, c, d \in\{-1,0,1,2,3, \ldots \ldots, 10\}\), such that \(A=A^{-1}\), isJEE Mains 2022 Hard
- If \(\operatorname{gcd}( m , n )=1\) and \(1^2-2^2+3^2-4^2+\ldots \ldots\) \(+(2021)^2-(2022)^2+(2023)^2=1012 m ^2 n\), then \(m ^2- n ^2\) is equal toJEE Mains 2023 Hard
- If \(\int_0^{\frac{\pi}{4}} \frac{\sin ^2 x}{1+\sin x \cos x} d x=\frac{1}{a} \log _e\left(\frac{a}{3}\right)+\frac{\pi}{b \sqrt{3}}\), where a, \(\mathrm{b} \in \mathrm{N}\), then \(\mathrm{a}+\mathrm{b}\) is equal to ...........JEE Mains 2024 Hard
- The integral \(\int_{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-\mathrm{x}}{1+\mathrm{x}}}\right) \mathrm{dx}\) is equal to :JEE Mains 2024 Medium
- The equation of the curve passing through the origin and satisfying the differential equation \(\left( {1 + {x^2}} \right)\,\frac{{dy}}{{dx}} + 2xy = 4{x^2}\) isJEE Mains 2013 Hard
- The number of real solutions of the equation \(x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0\) isJEE Mains 2024 Hard