Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #146
Evaluate \(\int_0^{\pi/2}(5\sin x+3\cos x)/(\sin x+\cos x)dx\).
✅ Step-by-Step Solution
Final Answer: 2π
- Write the ratio as 4+(sin x−cos x)/(sin x+cos x).
- The second term is −d ln(sin x+cos x)/dx and has equal endpoint log values 0. Thus I=4(π/2)=2π.
- Therefore the integral equals 2π.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Write the ratio as 4+(sin x−cos x)/(sin x+cos x).
- [1 mark] The second term is −d ln(sin x+cos x)/dx and has equal endpoint log values 0. Thus I=4(π/2)=2π.
- [0.5 marks] Therefore the integral equals 2π.
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