How do you use the second fundamental theorem of Calculus to find the derivative of given #int (t^2 +3t+2)dt# from #[-3, x]#?
The second Fundamental Theorem of Calculus enables us to find the function defined by
Find an antiderivative of
# = ((x)^3/3+(3(x)^2)/2+2(x))-((-3)^3/3+(3(-3)^2)/2+2(-3))#
# = x^3/3+(3x^2)/2+2x+3/2#
We get the same answer much more quickly by using part 1 of the fundamental theorem.