COMEDK · Maths · 30. Definite Integration
If \(\int_{a}^{b} \frac{x^{n}}{x^{n}+(16-x)^{n}} d x=6\), then
- A \(a=4, b=12, n \in R\)
- B \(a=2, b=14, n \in R\)
- C \(a=-4, b=20, n \in R\)
- D \(a=2, b=8, n \in R\)
Answer & Solution
Correct Answer
(B) \(a=2, b=14, n \in R\)
Step-by-step Solution
Detailed explanation
\(\int_{a}^{b} \frac{x^{n}}{x^{n}+(16-x)^{n}} d x=6...(i)\) Let \(a+b=16\), then \(\int_{a}^{b} \frac{(16-x)^{n}}{(16-x)^{n}+x^{n}} d x=6..(ii)\) Adding Eqs. (i) and (ii), we get \(\int_{a}^{b} 1 \cdot d x=12 \Rightarrow b-a=12\) Solving \(a+b=16\) and \(b-a=12\), we get…
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
- If \(A=\left[\begin{array}{cc}2-k & 2 \\ 1 & 3-k\end{array}\right]\) is a singular matrix, then the value of \(5 k-k^2\) isCOMEDK 2022 Easy
- \(\int x^x(1+\log x) d x\) is equal toCOMEDK 2023 Easy
- If \(\sin 3 \theta=\sin \theta\), how many solutions exist such that \(-2 \pi < \theta < 2 \pi\) ?COMEDK 2020 Medium
- The maximum of the function \(3 \cos x-4 \sin x\) isCOMEDK 2013 Easy
- If \({ }^n C_3=220\), then \(n=\) ?COMEDK 2022 Easy
- The solution of the differential equation
\(y \dfrac{d y}{d x}=x\left[\dfrac{y^{2}}{x^{2}}+\dfrac{\phi\left(\dfrac{y^{2}}{x^{2}}\right)}{\phi^{\prime}\left(\dfrac{y^{2}}{x^{2}}\right)}\right]\) is
(where, \(C\) is a constant)COMEDK 2021 Hard
More PYQs from COMEDK
- What would be the cell potential for the Galvanic cell which is represented by the electrochemical reaction:
\(\begin{aligned}
& 2 \mathrm{Cr}_{(\mathrm{S})}+3 \mathrm{Fe}^{2+}(0.02 \mathrm{M}) \rightarrow 2 \mathrm{Cr}^{3+}(0.2 \mathrm{M})+3 \mathrm{Fe} \\
& \mathrm{E}^0 \mathrm{Fe}^{2+} / \mathrm{Fe}=-0.42 \mathrm{~V} \quad \mathrm{E}^0 \mathrm{Cr}^{3+} / \mathrm{Cr}=-0.72 \mathrm{~V}
\end{aligned}\)COMEDK 2025 Medium - The parametric equation of a parabola is \(x=t^{2}+1, y=2 t+1\). The cartesian equation of its directrix isCOMEDK 2012 Easy
- Which of the following is correct mixture of azeotrope?COMEDK 2021 Medium
- In a \(L-C-R\) circuit the potential diffcrcnce between the terminals of the inductance is \(60 \mathrm{~V}\), between the terminals of the capacitor is \(30 \mathrm{~V}\) and that between the terminals of resistance is \(40 \mathrm{~V}\). The supply voltage will be equal toCOMEDK 2019 Medium
- Find the pole strength of a magnet of length \(2 \mathrm{~cm}\), if the magnetic field strength \(B\) at distance \(10 \mathrm{~cm}\) from the centre of a magnet on the axial line of the magnet is \(10^{-4} \mathrm{~T}\).COMEDK 2023 Medium
- If the sum of first \(n\) natural numbers is \(\frac{1}{78}\) times the sum their cubes, then the value of \(n\) isCOMEDK 2014 Easy