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

#### ewkimchi

Let
.
Find the MacLaurin polynomial of degree 5 for
.

Use this polynomial to estimate the value of
.

#### Bop

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

#### HallsofIvy

MHF Helper
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

I hadn't seen it was function of $$\displaystyle x$$, my mistake.

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