integrate 2^(t^2)

Question

integrate 2^(t^2)

astrophysics · Answer

$$\huge \int\limits 2^{t^2} dt?$$

anonymous · Answer

yeah I need to start using that feature more

anonymous · Answer

the question given is $$F(x)=\int\limits_{0}^{3x}f(t)dt$$

anonymous · Answer

where f(t)=2^(t^2)
calculate F(0)

anonymous · Answer

I can see why F(0) = 0, but i cant actually get to that conclusion if that makes any sense

astrophysics · Answer

You have to use the fundamental theorem of calculus

anonymous · Answer

so F'(x)=f(x) yeah?

astrophysics · Answer

You should start putting the images of the question, $$F(x) = \int\limits_{0}^{3x} f(t) dt $$ we then have $$F(x) = \int\limits_{0}^{3x} 2^{t^2} dt = F(3x)-F(0)$$

astrophysics · Answer

This applies the chain rule

astrophysics · Answer

$$\int\limits_{0}^{3x} \frac{ d }{ dx } f(t) dt$$ pretty much

anonymous · Answer

wait am i supposed to differentiate it or integrate it?

astrophysics · Answer

Depends on what the question is asking yhou

anonymous · Answer

part a is just asking for the value of F(0)

astrophysics · Answer

I'm assuming it's asking for the derivative

astrophysics · Answer

Use $$\int\limits_{0}^{3x} 2^{t^2}dt = F(3x)-F(0)$$ then

astrophysics · Answer

So yeah $$F' = f$$

anonymous · Answer

okay so obviously if F(0) when plugged in will give 0

anonymous · Answer

this problem is just worded weird

astrophysics · Answer

Your integral is not elementary though

astrophysics · Answer

Why don't you post the problem

anonymous · Answer

I will right now! I solved parts of it but now im on part c one sec let me type it

astrophysics · Answer

The other parts are most likely needed

anonymous · Answer

(a) Calculate F(0).
(b) Using n = 3 subintervals and left-hand endpoints, estimate the value of F(1). Begin
by calculating ∆t and filling in the table of values below.
       t 0 1 2 3
       f(t) 1 2 16 512           ∆t = ?
(c) Calculate F(x) and find the local linearization of F(x) about x = 0.
(d) Using part (c), estimate the value F(1) (this may not be a very good estimation).

anonymous · Answer

a) 0
b) well i kinda already put the values in and delta t is 1
im stuck on c

astrophysics · Answer

How did you do the first one

astrophysics · Answer

They want $$F(0) = \int\limits_{0}^{3x} stuff dt$$

anonymous · Answer

F(x)=f'(x) so d/dx of 2^(t^2) is (2^(x^2))(xlog(2)) so when x is zero then the whole thing is equal to zero