AP EAMCET · Maths · Indefinite Integration
If \(A=\int_0^{\infty} \frac{1+x^2}{1+x^4} d x, \quad B=\int_0^1 \frac{1+x^2}{1+x^4} d x\), then
- A \(2 \mathrm{~A}=\mathrm{B}\)
- B \(\mathrm{A}=\mathrm{B}\)
- C \(2 \mathrm{~B}=\mathrm{A}\)
- D \(2 \mathrm{~B}+\mathrm{A}=0\)
Answer & Solution
Correct Answer
(C) \(2 \mathrm{~B}=\mathrm{A}\)
Step-by-step Solution
Detailed explanation
\(A=\int_0^{\infty} \frac{1+x^2}{1+x^4} d x, B=\int_0^1 \frac{1+x^2}{1+x^4} d x\) Let \(I=\int \frac{1+x^2}{1+x^4} d x=\int \frac{1+x^2}{\left(x^2-\sqrt{2} x+1\right)\left(x^2+\sqrt{2} x+1\right)} d x\) By partial fraction…
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
- \(A=\left[\begin{array}{lll}0 & 1 & 2 \\ 2 & 3 & 0 \\ 4 & 0 & 3\end{array}\right]\) and \(B\) is a matrix such that \(A B=B A\). If
\(A B\) is not an identity matrix, then the matrix that can be taken as B isAP EAMCET 2024 Easy - Let \((x, y) \in R \times R\) and \(\bar{a}=x \bar{i}+2 \bar{j}-\bar{k}, \bar{b}=6 \bar{i}-y \bar{j}+2 \bar{k}\) be two vectors. If \(|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|^2+|\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}|^2=\mathrm{f}(\mathrm{x}) \mathrm{g}(\mathrm{y})\), then \(\mathrm{f}(\mathrm{x})+\mathrm{g}(\mathrm{y})-46=0\) representsAP EAMCET 2025 Medium
- \(\int \frac{\sin (x-a)}{\sin (x-b)} d x=A x+B \log |\sin (x-b)|+C \Rightarrow(A, B)=\)AP EAMCET 2017 Hard
- A value of \(c\) according to the Lagrange's mean value theorem for \(f(x)=(x-1)(x-2)(x-3)\) in \([0,4]\) isAP EAMCET 2024 Medium
- If \(A\) is in the third quadrant and \(\tan A=\frac{\sqrt{7}}{3}\), then \(18-16 \sin ^2 \frac{A}{2}-32 \sin \frac{A}{2} \sin \frac{5 A}{2}=\)AP EAMCET 2018 Medium
- If \(A=\left[\begin{array}{ccc}-1 & x & -3 \\ 2 & 4 & z \\ y & 5 & -6\end{array}\right]\) is a symmetric matrix and \(B=\left[\begin{array}{ccc}0 & 2 & q \\ p & 0 & -4 \\ -3 & r & s\end{array}\right]\) is a skew symmetric matrix, then \(|A|+|B|-|A B|=\)AP EAMCET 2025 Medium
More PYQs from AP EAMCET
- A steel rod of radius \(20 \mathrm{~mm}\) and length of \(2 \mathrm{~m}\) is acted upon by a force of \(400 \mathrm{kN}\) along the length. The values of stress and strain are respectively
\(\left(Y_{\text {steel }}=2 \times 10^{11} \mathrm{Nm}^{-2}\right)\)AP EAMCET 2023 Easy - Two capacitors of capacities \(1 \mu \mathrm{F}\) and \(C \mu \mathrm{F}\) are connected in series and the combination is charged to a potential difference of \(120 \mathrm{~V}\). If the charge on the combination is \(80 \mu \mathrm{C}\), the energy stored in the capacitor of capacity \(C\) in \(\mu \mathrm{J}\) isAP EAMCET 2010 Medium
- The two pairs of straight lines \(12 x^2+7 x y-12 y^2=0\) and \(12 x^2+7 x y-12 y^2-x+7 y-1=0\) constitute aAP EAMCET 2022 Medium
- If \(\vec{a}=-4 \hat{i}+2 \hat{j}+4 \hat{k}, \vec{b}=\sqrt{2} \hat{i}-\sqrt{2} \hat{j}\) are two vectors then angle between the vectors \(2 \vec{a}\) and \(\frac{\vec{b}}{2}\) isAP EAMCET 2024 Easy
- The elastic energy stored per unit volume in terms of longitudinal strain ' \(\epsilon\) ' and Young's modulus ' \(Y\) ' isAP EAMCET 2024 Easy
- In an amino acid, the carboxylic group ionises at \(\mathrm{pH}=2.56\left(\mathrm{pK}_{\mathrm{a}_1}\right)\) and ammonium ion ionises at \(\mathrm{pH}=9.38\left(\mathrm{pK}_{\mathrm{a}_2}\right)\). The isoelectric point of the amino acid is atAP EAMCET 2021 Medium