Question

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

Short answer

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

Step-by-step solution

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.

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: \(d/dt (e^t + C) = e^t\).

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.