Question

Don't really need an answer just an explanation.
integral(x^2)dx.
Is f(x) = x^2 ?

Answer 1

I thought that f'(x) = x^2 because the derivative of an integral is the inside stuff.
however in my book this is one of the questions and it says that f(x) = x^2. Can someone explain?

Answer 2

Is the question

\[\int\limits_{}^{} x ^{2} dx\]

?

Answer 3

yes;

Answer 4

yeah i know the antiderivative of the function. i just don't know why in the book it says that f(x) = x^2

Answer 5

What is the question, exactly?

Answer 6

It could possibly be a typo.

Answer 7

Or it could be asking you to integrate f(x) which is x squared? I'm a little unclear about what you're asking.

Answer 8

what u typed. @LogicalApple

Answer 9

oh use simpson's rule and trapezoidal rule error stuff

Answer 10

with n = 4

Answer 11

Oh ok. But what are the limits?

Answer 12

0-2

Answer 13

this is the work they have

Answer 14

Simpsons Rule:
\[\int\limits_{a}^{b}f(x)dx \approx \frac{ \Delta x }{ 3 }[f(x_0)+4f(x_1)+2f(x_2)+...+2f(x_{n-2})+4f(x_{n-1})+f(x_n)\]

Answer 15

\[\int\limits_{0}^{2}x^3dx\]
sorry i typed the original question wrong. :((

Answer 16

yeah i know how to use simpson and trapezoid rule formulas and errors stuff

Answer 17

In the Trapezoid Rule u approximate the curve with a straight line.
For Simpson’s Rule u approximate the function with a quadratic.

Answer 18

i just can't figure out why they put f(x) = x^3

Answer 19

sorry i'm gonna go off for a few (20 max) minutes. i'll be back.

Answer 20

sorry i had a little trouble with my login on my laptop.
-_- okay everyone left... :(

Answer 21

f(x) stands for the function in terms of x
f'(x) is the derivative of function
f''(x) is the second derivative
etc. Hope that helps

Answer 22

haha thanks but i know what those mean
just the question is really frustrating...
because they used f(x) = x^3 when it said integral from 0 to 2 of x^3 and they said that f(x) = x^3 but i have no idea why...
cuz i thought that f'(x) = x^3.
oh btw i'm viewing this question. it just doesn't say so cuz i'm replying thru my homepage.

Answer 23

\[\int f(x)dx\]
\[\int x^3dx\]
\[f(x)=x^3\]

Answer 24

@satellite73 could you explain why f(x) = x^3 ?
cuz i thought the derivative of the integral is just the inside part...

Answer 25

i am not sure exactly what you mean. it is true that the derivative of the integral is the integrand, but that means the derivative of
\[\int_a^xf(t)dt=f(x)\]
you have \[\int f(x)dx=\int x^3dx\] so \(f(x)=x^3\)

Answer 26

if \(f(x)=\sin(x)\) then
\[\int f(x)dx=\int\sin(x)dx\]

Answer 27

maybe i'm just confusing myself...
ohhh, ok i get it... :D

Answer 28

from your attachment f(x) is x^3
f'(x)=3x^2

Answer 29

-_- that was the part i was originally confused on, but now it makes more sense.
:)

Answer 30

it seems you are confusing f(x) with integral or antiderivative of f(x) sometimes denoted as F(x)
so F'(x) = f(x)
f(x) is the integrand or "inside part"

Answer 31

yes that was what i was confused about @dumbcow
ohhhhh yeah i was thinking F'(x) = x^3 but i guess i didn't think of it as f(x)
thanks :D