Mathematics
Mathematics
Problem
State the rule for the indefinite integral of the sum or difference of two differentiable functions.Intuitive explanation
The key insight is that integration is a linear operation—it respects addition and subtraction just like differentiation does. When you integrate a sum or difference, you can split it apart and integrate each piece separately, then combine the results. This works because the derivative of a sum is the sum of derivatives, so reversing that process (integration) must also preserve this structure.
Intuitive explanation
The key insight is that integration is a linear operation—it respects addition and subtraction just like differentiation does. When you integrate a sum or difference, you can split it apart and integrate each piece separately, then combine the results. This works because the derivative of a sum is the sum of derivatives, so reversing that process (integration) must also preserve this structure.