anonymous
  • anonymous
integrate 2^(t^2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Astrophysics
  • Astrophysics
\[\huge \int\limits 2^{t^2} dt?\]
anonymous
  • anonymous
yeah I need to start using that feature more
anonymous
  • anonymous
the question given is \[F(x)=\int\limits_{0}^{3x}f(t)dt\]

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anonymous
  • anonymous
where f(t)=2^(t^2) calculate F(0)
anonymous
  • anonymous
I can see why F(0) = 0, but i cant actually get to that conclusion if that makes any sense
Astrophysics
  • Astrophysics
You have to use the fundamental theorem of calculus
anonymous
  • anonymous
so F'(x)=f(x) yeah?
Astrophysics
  • Astrophysics
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
  • Astrophysics
This applies the chain rule
Astrophysics
  • Astrophysics
\[\int\limits_{0}^{3x} \frac{ d }{ dx } f(t) dt\] pretty much
anonymous
  • anonymous
wait am i supposed to differentiate it or integrate it?
Astrophysics
  • Astrophysics
Depends on what the question is asking yhou
anonymous
  • anonymous
part a is just asking for the value of F(0)
Astrophysics
  • Astrophysics
I'm assuming it's asking for the derivative
Astrophysics
  • Astrophysics
Use \[\int\limits_{0}^{3x} 2^{t^2}dt = F(3x)-F(0)\] then
Astrophysics
  • Astrophysics
So yeah \[F' = f\]
anonymous
  • anonymous
okay so obviously if F(0) when plugged in will give 0
anonymous
  • anonymous
this problem is just worded weird
Astrophysics
  • Astrophysics
Your integral is not elementary though
Astrophysics
  • Astrophysics
Why don't you post the problem
anonymous
  • anonymous
I will right now! I solved parts of it but now im on part c one sec let me type it
Astrophysics
  • Astrophysics
The other parts are most likely needed
anonymous
  • anonymous
(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
  • anonymous
a) 0 b) well i kinda already put the values in and delta t is 1 im stuck on c
Astrophysics
  • Astrophysics
How did you do the first one
Astrophysics
  • Astrophysics
They want \[F(0) = \int\limits_{0}^{3x} stuff dt\]
anonymous
  • anonymous
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

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