Section 5.2 : Computing Indefinite Integrals
1. Evaluate \( \displaystyle \int{{4{x^6} - 2{x^3} + 7x - 4\,dx}}\).
Show SolutionThere really isn’t too much to do other than to evaluate the integral.
\[\int{{4{x^6} - 2{x^3} + 7x - 4\,dx}} = \frac{4}{7}{x^7} - \frac{2}{4}{x^4} + \frac{7}{2}{x^2} - 4x + c = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{4}{7}{x^7} - \frac{1}{2}{x^4} + \frac{7}{2}{x^2} - 4x + c}}\]Don’t forget to add on the “+c” since we know that we are asking what function did we differentiate to get the integrand and the derivative of a constant is zero and so we do need to add that onto the answer.