Integrals

⭐ Important Questions

1. Evaluate ∫(3x² + 2x + 1)dx.
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   ∫(3x² + 2x + 1)dx = x³ + x² + x + C
2. Evaluate ∫_0¹ (x² + 1)dx.
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   ∫_0¹ (x² + 1)dx = [x³/3 + x]_0¹ = 4/3
3. Find ∫e^x sin x dx.
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   I = ∫e^x sin x dx = e^x sin x - ∫e^x cos x dx\n= e^x sin x - (e^x cos x + ∫e^x sin x dx)\n= e^x(sin x - cos x) - I\n2I = e^x(sin x - cos x)\nI = e^x(sin x - cos x)2 + C