Monomath – CBSE | GSEB | IB | JEE Maths by Ajay Yadav (Math King of Katargam) – 15+ Years Experience. Study Notes, Video Lessons, Formula Sheets & PYQs.

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Integrals

Previous Year Questions (2022-2024)

📅 Year 2022

Evaluate ∫(3x² + 2x + 1)dx.
Show Solution
∫(3x² + 2x + 1)dx = x³ + x² + x + C
Evaluate ∫_0¹ (x² + 1)dx.
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∫_0¹ (x² + 1)dx = [x³/3 + x]_0¹ = 4/3

📅 Year 2023

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
Evaluate ∫(3x² + 2x + 1)dx.
Show Solution
∫(3x² + 2x + 1)dx = x³ + x² + x + C

📅 Year 2024

Evaluate ∫_0¹ (x² + 1)dx.
Show Solution
∫_0¹ (x² + 1)dx = [x³/3 + x]_0¹ = 4/3
Find ∫e^x sin x dx.
Show Solution
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