CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Q273 Marksindefinite_integrals
CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Question 27 (Integrals)
Evaluate \(\int\frac{3x-1}{\sqrt{x^2-4x}}\,dx\).
✅ Step-by-Step Solution
Final Answer: 3√(x²−4x)+5 ln |x−2+√(x²−4x)|+C on x<0 or x>4.
- Write 3x−1=(3/2)(2x−4)+5 and x²−4x=(x−2)²−4.
- The first part integrates to 3√(x²−4x). The second uses the logarithmic primitive of 1/√(u²−4) for u=x−2.
- Combine the terms, with independent constants on the two real components.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write 3x−1=(3/2)(2x−4)+5 and x²−4x=(x−2)²−4.
- [2 marks] The first part integrates to 3√(x²−4x). The second uses the logarithmic primitive of 1/√(u²−4) for u=x−2.
- [0.5 marks] Combine the terms, with independent constants on the two real components.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
On a stormy day a sniper is three times as likely to hit as to miss…
Next Question →Evaluate \(\int_{\pi/12}^{5\pi/12}\frac{dx}{1+\sqrt{\cot x}}\). OR…
All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/2/3
Related Questions in Integrals
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int x^2e^{x^3}\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(1+x)\sec^2(xe^x)\,dx\) on an interval where defined.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int e^x(\cos x-\sin x)\,dx\).
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int dx/(\sin^2x\cos^2x)\) on an interval avoiding its poles.
Class 12 Integrals · Mcq Single Correct
If \(\int\frac{3e^x-5e^{-x}}{4e^x+5e^{-x}}dx=ax+b\ln|4e^x+5e^{-x}|+C\), find a,b.
Class 12 Integrals · Mcq Single Correct
Evaluate \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).