Integrate 3t^2 + 7t with respect to t, between 1 and three.

To integrate you add one to the power and divide by the new power, so this becomes:3t³/3 + 7t²/2 simplifying to t³ + 7/2 t²If we were just performing indefinite integration you would need to remember the "+c" constant term. However since we are doing definite integration, this involves subtracting two solutions from each other and so the "+c" terms cancell and so can be ignored. [ t³ + 7/2 t²]³₁ = ((3)³+7/2 (3)²)-((1)³+7/2 (1)²) = 58.5-4.5= 54