Let F(x)=int_{0}^{x}(e^{{3t})^{4}}

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

Question

Let F(x)=int_{0}^{x}(e^{{3t})^{4}}

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

anonymous · Answer

please help

zarkon · Answer

where are you stuck?

anonymous · Answer

i dont exactly know how to put in the answer

zarkon · Answer

what do you mean 'put in the answer'?

anonymous · Answer

ok  please solve it and i can see your answer then compare to mine

zarkon · Answer

why don't you give me yours and I'll tell you if you are correct

anonymous · Answer

ok hold on

anonymous · Answer

629856 e^(81 t^4) t^3 (35+10530 t^4+524880 t^8+5668704 t^12)

anonymous · Answer

thats e^(−3t)^4 to the 5th degree

zarkon · Answer

why do you have t's

zarkon · Answer

F is a function of x

anonymous · Answer

well i do not know how to integrate e^(−3t)^4

zarkon · Answer

you don't need to

zarkon · Answer

just for clarification is it 

$$\int\limits_{0}^{x}e^{(3t)^4}dt$$
or 
$$\int\limits_{0}^{x}\left(e^{3t}\right)^4dt$$

anonymous · Answer

the first one

zarkon · Answer

ok..I'll get you started...

$$F(0)=\int\limits_{0}^{0}e^{(3t)^4}dt=0$$

$$\frac{d}{dx}F(x)=\frac{d}{dx}\int\limits_{0}^{x}e^{(3t)^4}dt=e^{(3x)^4}$$

$$F'(0)=1$$

anonymous · Answer

972e^(81x^4) (x^2+108x^6)

anonymous · Answer

is that the second derivative ?

anonymous · Answer

?

zarkon · Answer

$$324x^3e^{81x^4}$$

anonymous · Answer

do you mind explaining that, because i double checked with wolf ram alpha and i got my answer

anonymous · Answer

actually your answer is the first derivative. Isnt it ?

anonymous · Answer

?

anonymous · Answer

so is my answer 1944e^(81x^4)(1+(2754x^4)+(314928x^8)+5668704x^12)

anonymous · Answer

or f(0) of that which is 1944

anonymous · Answer

because according to my program, none of those answers are right

anonymous · Answer

?

zarkon · Answer

972e^(81x^4) (x^2+108x^6) is the 3rd derivative not the 2nd