Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #145
Evaluate \(\int_0^{\pi/4}(\sin x+\cos x)/(3+\sin2x)dx\).
✅ Step-by-Step Solution
Final Answer: (ln3)/4
- Let u=sin x−cos x, du=(sin x+cos x)dx. Then 3+sin2x=4−u² and bounds are −1,0.
- A primitive is (1/4)ln|(2+u)/(2−u)|. Its endpoint difference is −(1/4)ln(1/3)=(ln3)/4.
- Therefore the integral equals (ln3)/4.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Let u=sin x−cos x, du=(sin x+cos x)dx. Then 3+sin2x=4−u² and bounds are −1,0.
- [1 mark] A primitive is (1/4)ln|(2+u)/(2−u)|. Its endpoint difference is −(1/4)ln(1/3)=(ln3)/4.
- [0.5 marks] Therefore the integral equals (ln3)/4.
Master Chapter 7: Integrals
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Integrals.
← Previous Question
Prove that the convergent improper integral…
Next Question →Evaluate \(\int_0^{\pi/2}(5\sin x+3\cos x)/(\sin x+\cos x)dx\).
More Practice Questions in Integrals
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 \(\int_{-1}^{1}|x-2|/(x-2)\,dx\).