Problem 17 - College Algebra and Calculus: An Applied Approach

Question

Find the indefinite integral and check your result by differentiation. $$ \int e d t $$

Step-by-Step Solution

Answer

The indefinite integral of \(e^t\) is \(e^t + C\). This has been verified by differentiation.

Step 1: Integrate \(e^t\)

Integration of \(e^t\) can be done directly by applying the formula. So, \(\int e^t dt = e^t + C\), where C is the integration constant.

Step 2: Check the result by differentiation.

Differentiation is the reverse process of integration. To check the result, differentiate \(e^t + C\). So, the derivative of the integral metioned in the previous step is: \(d/dt (e^t + C) = e^t\).

Step 3: Compare the results.

If the result of the differentiation, i.e., \(e^t\), is same as the given integrand, then the original integration is concluded to be correct.