14 June 2026

🎯 INTEGRATION SHORTCUT TRICK

Question:
∫ (sin x + cos x)/√(sin 2x) dx

In this video, we solve a beautiful trigonometric integration problem using a smart substitution technique.

Key Concepts Covered:
✅ Trigonometric identities
✅ Smart substitution
✅ Standard inverse trigonometric integration
✅ Graphical understanding of the function
✅ Exam-oriented shortcut method

Solution Outline:
Let u = sin x − cos x

Then,
du = (sin x + cos x) dx

Using:
(sin x − cos x)² = 1 − sin 2x

The integral becomes:
∫ du/√(1 − u²)

Applying the standard formula:

∫ du/√(1 − u²) = sin⁻¹(u) + C

Final Answer:
sin⁻¹(sin x − cos x) + C

Perfect for:
📚 JEE Main & Advanced
📚 NDA
📚 CUET
📚 CBSE Boards
📚 ISC & ICSE
📚 Engineering Entrance Exams

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✨ Learn Smart Tricks with A K Polai Sir ✨

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Видео 14 June 2026 канала Mathemagician_AKP