COMEDK · Maths · 28. Indefinite Integration
\(\int \sqrt{x^2-4 x+2} d x=\)
- A \((x-2) \sqrt{x^2-4 x+2}+\dfrac{1}{2} \log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C\)
- B \(\dfrac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C\)
- C \(\dfrac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\sin ^{-1} \dfrac{x-2}{\sqrt{2}}+C\)
- D \(\dfrac{1}{2}(x-2) \sqrt{x^2-4 x+2}+\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C\)
Answer & Solution
Correct Answer
(B) \(\dfrac{1}{2}(x-2) \sqrt{x^2-4 x+2}-\log \left|(x-2)+\sqrt{x^2-4 x+2}\right|+C\)
Step-by-step Solution
Detailed explanation
The integral is \(I = \int \sqrt{x^2 - 4x + 2} dx\). Complete the square inside the square root: \(x^2 - 4x + 2 = (x^2 - 4x + 4) - 2 = (x-2)^2 - 2\). Thus, \(I = \int \sqrt{(x-2)^2 - 2} dx\). Let \(u = x-2\), then \(du = dx\). The integral becomes \(I = \int \sqrt{u^2 - 2} du\).…
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 coefficient of \(x^{20}\) in the expansion of \(\left(1+3 x+3 x^2+x^3\right)^{20}\) isCOMEDK 2022 Easy
- If \(49^n+16^n+k\) is divisible by 64 for \(n \in N\), then the least negative integral value of \(k\) isCOMEDK 2023 Easy
- Area of the region bounded by the curve \(y=\cos x\) between \(x=-\dfrac{\pi}{2}\) and \(x=\pi\) is-----COMEDK 2025 Medium
- The vector that must be added to \(\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) and \(3 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-7 \hat{\mathrm{k}}\) so resultant vector is a unit vector along the \(X\) - axis isCOMEDK 2021 Medium
- The co-axial system of circles given by \(x^{2}+y^{2}+2 g x+c=0\) for \(c < 0\) representsCOMEDK 2013 Hard
- \(\text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|=\)COMEDK 2024 Easy
More PYQs from COMEDK
- When a mixture of calcium benzoate and calcium formate is dry distilled, we getCOMEDK 2019 Hard
- Which one of the following shows highest magnetic moment?COMEDK 2019 Easy
- Two identical conducting balls having unequal positive charges \(q_1\) and \(q_2\) are separated by a distance \(r\). If they are made to touch each other and then separated to the same distance, the force between them will beCOMEDK 2025 Medium
- 800 mL of a \(0.5 \mathrm{M} \mathrm{HNO}_3\) at 300 K is heated to a temperature of 350 K , its volume is reduced to one half and 10.5 g of \(\mathrm{HNO}_3\) is evaporated. Assuming complete ionization, the osmotic pressure of the remaining solution is: [Given \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) ]COMEDK 2025 Medium
- In a trial, the probability of success is twice the probability of failure. In six trials, the probability of at most two failure will beCOMEDK 2023 Medium
- A particle \(A\) has charge \(+q\) and particle \(B\) has charge \(+4 q\), each of them having the same mass \(m\). When allowed to fall from rest through the same electrical potential difference, then the ratio of their speeds will becomeCOMEDK 2015 Medium