Check whether (x + 1)² = 2(x − 3) is a quadratic equation.
🎯 Chapter Readiness Score35%
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⚡ Key Formulas at a Glance
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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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Standard Method4 Marks
Evaluate ∫ sin x / sin(x−a) dx.
▶ Show Detailed Solution
Let x − a = t ⇒ x = t + a. ∫ sin(t+a)/sin t dt = ∫ (sin t cos a + cos t sin a)/sin t dt = cos a × t + sin a log|sin t| + C = (x−a)cos a + sin a log|sin(x−a)| + C