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Integration and Differential Equations Basic Questions for AGNIVEER VAYU

Free, AI-curated practice for the Integration and Differential Equations Basic section of AGNIVEER VAYU. We have 12+ verified questions in this bank. Below: 5 sample questions. Sign up free to unlock unlimited practice + AI explanations + per-topic analytics.

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Sample questions

Q1 · medium · AI-verified
Evaluate: ∫ x⁴ dx
  1. x⁴/4 + C
  2. 4x³ + C
  3. x⁵/5 + C
  4. x⁵ + C
Q2 · hard · AI-verified
The integrating factor of the linear differential equation dy/dx − (2/x)y = x² is:
  1. e^(x²)
  2. 1/x
  3. x²
  4. 1/x²
Q3 · medium · AI-verified
Evaluate: ∫ (3x² − 2x + 5) dx
  1. 3x³ − x² + 5x + C
  2. x³ − 2x² + 5x + C
  3. 6x − 2 + C
  4. x³ − x² + 5x + C
Q4 · medium · AI-verified
Solve the differential equation dy/dx = y. Which of the following is the general solution?
  1. y = Ce^x
  2. y = Ce^(−x)
  3. y = Cx
  4. y = C + e^x
Q5 · easy · AI-verified
What is ∫e^x dx?
  1. e^x + C
  2. x·e^x + C
  3. e^x / x + C
  4. e^(x+1) + C
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