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Section 5-1 : Indefinite Integrals

7. Determine \(h\left( t \right)\) given that \(h'\left( t \right) = {t^4} - {t^3} + {t^2} + t - 1\).

Hint : Remember that all indefinite integrals are asking us to do is “undo” a differentiation.
Show Solution

We know that indefinite integrals are asking us to undo a differentiation to so all we are really being asked to do here is evaluate the following indefinite integral.

\[h\left( t \right) = \int{{h'\left( t \right)\,dt}} = \int{{{t^4} - {t^3} + {t^2} + t - 1\,dt}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{5}{t^5} - \frac{1}{4}{t^4} + \frac{1}{3}{t^3} + \frac{1}{2}{t^2} - t + c}}\]

Don’t forget the “+c”! Remember that the original function may have had a constant on it and the “+c” is there to remind us of that.