🏆 Daily Math Board Challenge (2026 Edition)
Check whether (x + 1)² = 2(x − 3) is a quadratic equation.
🎯 Chapter Readiness Score35%
⚡ Key Formulas at a Glance
Formula (Hover/Click)
Power Rule Integral
∫ xⁿ dx = (xⁿ⁺¹ / n+1) + C for n ≠ −1
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Integration by Parts
∫ u v dx = u ∫ v dx − ∫ [u' (∫ v dx)] dx
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King Property (Definite)
∫₀ᵃ f(x) dx = ∫₀ᵃ f(a−x) dx
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Special Integral 1
∫ dx / (x² + a²) = (1/a) tan⁻¹(x/a) + C
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Special Integral 2
∫ dx / √(a² − x²) = sin⁻¹(x/a) + C
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1NCERT Class 12 Ex 7.1 Q1
Find anti-derivative (integral) of sin 2x using method of inspection.
▶ Show Detailed Solution
Since d/dx (cos 2x) = −2 sin 2x ⇒ sin 2x = −½ d/dx (cos 2x) = d/dx (−½ cos 2x).
Anti-derivative = −½ cos 2x + C ■