Why is f'(x) not t³ for this integral problem?

[beanryu]

HI people, this will be kindergarden homework for you guys. PLease help! THANKS a lot!

S=integral sign

10
S t^3 dt=f(x)
x

f'(x)=?
I say f'(x)=t^3, but it's not correct. WHY?

 

[chroot]

First, find the indefinite integral of t³ dt, then evaluate it from t=x to t=10. Only after you've completed that can you differentiate the resultant expression with respect to x.

- Warren

 

[beanryu]

so the indefinite integral of t^3 dt is t^4/4

then evaluate it from t=x to t=10

10^4/4-x^4/4

then differentiate this expression

0-x^3

it's correct!... I am dumb THANX a lot fOR The fAsT repLY !

 

[chroot]

You're not dumb at all. See, you just learned something. :)

- Warren