# Let #F(x)=int_0^x e^(-5t^4)dt#. Find the MacLaurin polynomial of degree 5 for F(x)?

##### 1 Answer

May 5, 2018

#### Explanation:

Using Fundamental Theorem of Calculus:

By definition:

Integrating:

# F(x)= C + x - x^5 + mathbb O(x^9) #

And:

#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.