Find the MacLaurin polynomial of degree 5 for F(x).

Apr 2010
57
1
Let
.
Find the MacLaurin polynomial of degree 5 for
.

Use this polynomial to estimate the value of
.
 

Bop

Dec 2009
48
0
Hello, just solve the integral and apply MacLaurin series. And in order to calculate the define integral just replace the values.
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Don't solve the integral (it cannot be done in terms of elementary functions, anyway)! You only need the value of F at x= 0 which is obviously 0 because \(\displaystyle \int_0^0 f(x)dx= 0\) for any f.

Then use the Fundamental Theorem of Calculus to find F'(x) and differentiate that to get F", F''', F'''', and F'''''.
 

Bop

Dec 2009
48
0
I hadn't seen it was function of \(\displaystyle x\), my mistake.