JEE Mains · Maths · STD 12 - 8. Application and integration
The area bounded by the curves \(y=\left|x^{2}-1\right|\) and \(y=1\) is.
- A \(\frac{2}{3}(\sqrt{2}+1)\)
- B \(\frac{4}{3}(\sqrt{2}-1)\)
- C \(2(\sqrt{2}-1)\)
- D \(\frac{8}{3}(\sqrt{2}-1)\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{3}(\sqrt{2}-1)\)
Step-by-step Solution
Detailed explanation
Area \(=\) ABCDEA \(=2\left(\int_{0}^{1}\left(1-\left(1-x^{2}\right)\right) d x+\int_{1}^{\sqrt{2}}\left(1-\left(x^{2}-1\right)\right) d x\right)\) \(=\frac{8}{3}(\sqrt{2}-1)\)
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 number of points, at which the function \(f ( x )\) \(=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|, x \in R\) is not differentiable, is ............JEE Mains 2021 Medium
- If \(n\) is the number of irrational terms in the expansion of \(\left(3^{1 / 4}+5^{1 / 8}\right)^{60},\) then \(( n -1)\) is divisible byJEE Mains 2021 Hard
- Let \(f(x)=(x+3)^2(x-2)^3, x \in[-4,4]\). If \(M\) and \(m\) are the maximum and minimum values of \(f\), respectively in \([-4,4]\), then the value of \(M-m\) is :JEE Mains 2024 Hard
- Let \( a_{1}, a_{2}, a_{3},..... \) be a G.P. of increasing positive terms such that \( a_{2} . a_{3} . a_{4}=64 \) and \( a_{1}+a_{3}+a_{5}=\frac{813}{7} \).
Then \( a_{3}+a_{5}+a_{7} \) is equal to:JEE Mains 2026 Hard - Let \(S=\{1,2,3,4\}\). Then the number of elements in the set \(\{f: S \times S \rightarrow S: f\) is onto and \(f(a, b)=f(b, a)\) \(\geq a; \forall(a, b) \in S \times S\}\) isJEE Mains 2022 Hard
- The sum of an infinite geometric series with positive terms is \(3\) and the sum of the cubes of its terms is \(\frac {27}{19}\). Then the common ratio of this series isJEE Mains 2019 Hard
More PYQs from JEE Mains
- The mean and variance of \(5\) observations are \(5\) and \(8\) respectively. If \(3\) observations are \(1,3,5\), then the sum of cubes of the remaining two observations isJEE Mains 2023 Hard
- The value of \(\lim_{x \to 0}\left(\dfrac{x^2\sin^2 x}{x^2 - \sin^2 x}\right)\) is:JEE Mains 2026 Medium
- A straight line \(L\) at a distance of \(4\) units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of \(60^o\) with the line \(x + y = 0\). Then an equation of the line \(L\) isJEE Mains 2019 Hard
- If \(1+\left(1-2^{2} \cdot 1\right)+\left(1-4^{2} \cdot 3\right)+\left(1-6^{2} \cdot 5\right)+\ldots \ldots+\left(1-20^{2} \cdot 19\right)\) \(=\alpha-220 \beta,\) then an ordered pair \((\alpha, \beta)\) is equal toJEE Mains 2020 Medium
- Let a differentiable function f satisfy the equation \( \int_{0}^{36}f(\frac{tx}{36})dt=4\alpha f(x) \). If \( y=f(x) \) is a standard parabola passing through the points (2, 1) and \( (-4,\beta) \),Then \( \beta^{\alpha} \) is equal to ___ .JEE Mains 2026 Medium
- If the mirror image of the point \((1,3,5)\) with respect to the plane \(4 x -5 y +2 z =8\) is \((\alpha, \beta, \gamma)\) then \(5(\alpha+\beta+\gamma)\) equals ...... ..JEE Mains 2021 Hard