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
