Let #F(x)=int_0^x e^(-5t^4)dt#. Find the MacLaurin polynomial of degree 5 for F(x)?
Using Fundamental Theorem of Calculus:
# F(x)= C + x - x^5 + mathbb O(x^9) #
#F(0) = 0 implies C = 0#
You can get the same result by evaluating a whole series of derivatives and calculating as the Maclaurin Series:
But I would not recommend it.