JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region \(\left\{( x , y ):\left| x ^2-2\right| \leq y \leq x \right\}\) is \(A\), then \(6 A +16 \sqrt{2}\) is equal to \(...........\).
- A \(26\)
- B \(25\)
- C \(27\)
- D \(24\)
Answer & Solution
Correct Answer
(C) \(27\)
Step-by-step Solution
Detailed explanation
\(\left|x^2-2\right| \leq y \leq x\) \(A=\int \limits_1^{\sqrt{2}}\left(x-\left(2-x^2\right)\right) d x+\int \limits_{\sqrt{2}}^2\left(x-\left(x^2-2\right)\right) d x\)…
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
- Let \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}-1}=28,{ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}=56\) and \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}+1}=70\). Let \(\mathrm{A}(4 \cos t, 4 \sin t), \mathrm{B}(2 \sin t,-2 \cos \mathrm{t})\) and \(C\left(3 r-n, r^2-n-1\right)\) be the vertices of a triangle \(A B C\), where \(t\) is a parameter. If \((3 x-1)^2+(3 y)^2\) \(=\alpha\), is the locus of the centroid of triangle ABC , then \(\alpha\) equalsJEE Mains 2025 Hard
- Then sum \(\sum\limits_{k = 1}^{20} {k\frac{1}{{{2^k}}}} \) is equal toJEE Mains 2019 Hard
- A natural number has prime factorization given by \(n =2^{ x } 3^{ y } 5^{ z },\) where \(y\) and \(z\) are such that \(y+z=5\) and \(y^{-1}+z^{-1}=\frac{5}{6}, y > z\). Then the number of odd divisors of \(n\), including \(1,\) is ..... .JEE Mains 2021 Hard
- The real number \(k\) for which the equation, \(2{x^2} + 3x + k = 0\) has two distinct real roots in \([0, 1]\)JEE Mains 2013 Hard
- Let \(A\) be the sum of the first \(20\) terms and \(B\) be the sum of the first \(40\) terms of the series \({1^2} + 2 \cdot {2^2} + {3^2} + 2 \cdot {4^2} + {5^2} + .\;.\;.\;.\).If \(B - 2A = 100\lambda \) then \(\lambda \) is equal to :JEE Mains 2018 Hard
- Let \(0 < z < y < x\) be three real numbers such that \(\frac{1}{ x }, \frac{1}{ y }, \frac{1}{ z }\) are in an arithmetic progression and \(x\), \(\sqrt{2} y, z\) are in a geometric progression. If \(x y+y z\) \(+z x=\frac{3}{\sqrt{2}} x y z\), then \(3(x+y+z)^2\) is equal to \(............\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- The foci of a hyperbola are \(( \pm 2,0)\) and its eccentricity is \(\frac{3}{2}\). A tangent, perpendicular to the line \(2 x+3 y=6\), is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the \(x\) - and \(y\)-axes are \(a\) and \(b\) respectively, then \(|6 a|+|5 b|\) is equal to \(..........\).JEE Mains 2023 Hard
- The magnitude of the projection of the vector \(2\hat i + 3\hat j + \hat k\) on the vector perpendicular to the plane containing the vectors \(\hat i + \hat j + \hat k\) and \(\hat i + 2\hat j + 3\hat k\) isJEE Mains 2019 Hard
- Let \(f:[-1,2] \rightarrow \mathrm{R}\) be given by \(f(x)=2 x^2+x+\left[x^2\right]-[x]\), where \([t]\) denotes the greatest integer less than or equal to \(t\). The number of points, where \(f\) is not continuous, is :JEE Mains 2024 Hard
- The sum of all integral values of \(\mathrm{k}(\mathrm{k} \neq 0\) ) for which the equation \(\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}\) in \(x\) has no real roots, is ..... .JEE Mains 2021 Hard
- The value of \(\tan ^{-1}\left(\frac{\cos \left(\frac{15 \pi}{4}\right)-1}{\sin \left(\frac{\pi}{4}\right)}\right)\) is equal toJEE Mains 2022 Easy
- Let \(\vec{a}\) and \(\vec{b}\) be the vectors of the same magnitude such that \(\frac{|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|}{|\vec{a}+\vec{b}|-|\vec{a}-\vec{b}|}=\sqrt{2}+1\). Then \(\frac{|\vec{a}+\vec{b}|^2}{|\vec{a}|^2}\) is :JEE Mains 2025 Medium