Class 12 Integrals · Short Answer2 Marksdefinite_integration
Class 12 Maths · Integrals · Short Answer #148
Evaluate \(\int_0^{\pi/2}e^x(\sin x-\cos x)dx\).
✅ Step-by-Step Solution
Final Answer: 1
- The derivative of −e^x cos x is e^x(sin x−cos x).
- At π/2 this primitive is 0; at 0 it is −1, so the difference is 1.
- Therefore the integral equals 1.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] The derivative of −e^x cos x is e^x(sin x−cos x).
- [1 mark] At π/2 this primitive is 0; at 0 it is −1, so the difference is 1.
- [0.5 marks] Therefore the integral equals 1.
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