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What is the solution of the equation dy/dx = 3x^2?

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Question: What is the solution of the equation dy/dx = 3x^2?

Options:

  1. y = x^3 + C
  2. y = 3x^3 + C
  3. y = x^2 + C
  4. y = 3x^2 + C

Correct Answer: y = x^3 + C

Solution: 

Integrating both sides gives y = ∫3x^2 dx = x^3 + C.

What is the solution of the equation dy/dx = 3x^2?

Practice Questions

Q1
What is the solution of the equation dy/dx = 3x^2?
  1. y = x^3 + C
  2. y = 3x^3 + C
  3. y = x^2 + C
  4. y = 3x^2 + C

Questions & Step-by-Step Solutions

What is the solution of the equation dy/dx = 3x^2?
  • Step 1: Start with the equation dy/dx = 3x^2.
  • Step 2: Recognize that dy/dx means the derivative of y with respect to x.
  • Step 3: To find y, we need to integrate both sides of the equation.
  • Step 4: Write the integral: y = ∫3x^2 dx.
  • Step 5: Calculate the integral of 3x^2. The integral of x^n is (x^(n+1))/(n+1). Here, n = 2.
  • Step 6: So, ∫3x^2 dx = 3 * (x^(2+1))/(2+1) = 3 * (x^3)/3 = x^3.
  • Step 7: Don't forget to add the constant of integration, C, to the result.
  • Step 8: Therefore, the solution is y = x^3 + C.
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