Sorry I know this should be easy, but what is the integral of U/du?
No worries, I'm here to help! To find the integral of U/du, you can use a method called substitution. Substitution allows you to rewrite the integrand in terms of a new variable. Here's the step-by-step process:
1. Let's start by rewriting the integrand: U/du.
2. Take the derivative of U to find dU. This allows us to determine what to substitute for du.
3. Once you have dU, rewrite the integral in terms of U and dU.
4. Evaluate the integral using the new variable U.
Let me walk you through it:
1. Rewrite the integrand: U/du
2. Take the derivative of U to find dU:
dU = d(U) / du
3. Rewrite the integral in terms of U and dU:
∫(U/du) = ∫(1/du) * U
4. Evaluate the integral using the new variable U:
∫(1/du) * U = ∫(1/dU) * U
This integral simplifies to:
∫(1/dU) * U = ∫1 dU = U + C
Therefore, the integral of U/du is U + C. Remember to add the constant of integration, "C," when you evaluate indefinite integrals.