Question

Calculate the indefinite integral : (assume t > a and t >

Answer 1

So here's your problem: $\int\limits {[t(t-a)(t-b)]} \, dt$.  The easiest way to do this is to distribute that whole thing out by FOIL-ing to get $\int\limits {t^3-t^2b-t^2a+abt} \, dt$.  Now the integration is straightforward. We are integrating with respect to t, so treat a and b like "regular" numbers.  Your integration, before simplifying, is $\frac{t^4}{4}- \frac{bt^3}{3}- \frac{at^3}{3}+ \frac{abt^2}{2}$.  Those 2 terms in the middle have the same denominator and power on the t, so we will combine those as like to get $\frac{t^4}{4}- \frac{abt^3}{3}+ \frac{abt^2}{2}+C$