Question

If the derivative of f is given by f'(x) = (tan^2 x)/ (x^2+1) and f(1) = 1/2, then f(0) =?

Answer 1

\[\int\limits_{}^{}\frac{\tan^2(x)}{x^2+1} dx\]
we need to look at integrating this

Answer 2

Are you sure it's \(\frac{\tan^2(x)}{x^2+1}\), I don't seem to be able to integrate that. It would be nicer if it was arctan instead of tan^2. :P

Answer 3

I thought this was a FToC problem, which I kinda suck at...

Answer 4

FToC?

Answer 5

fundamental theorem of calculus

Answer 6

Actually it is in a way or another.

Answer 7

Right, so no need to integrate then, yes?

Answer 8

We need to integrate.

Answer 9

well wolfram quit

Answer 10

We can find the value of f(0) numerically.

Answer 11

yeah im sure its tan^2 x

Answer 12

Call the definite integral \(\large \int_0^1 \frac{\tan^2(x)}{1+x^2}\) I, then:
\[f(1)-f(0)=I \implies f(0)=f(1)-I\].
Now, try to evaluate I using any numerical method and solve substitute into the equation above.

Answer 13

wat do u mean by any numerical method

Answer 14

It's a method to finding approximate value for the integral. Try using Simpson's rule; it's easy and efficient.

Answer 15

See here http://bit.ly/wg8SD3

Answer 16

This is an approximate value for the integral, you can use it to find f(0).

Answer 17

is it possible to get taht number without teh calcuator?

Answer 18

What number?

Answer 19

0.34456....which is the numeraical value of taht integral

Answer 20

Yes, you can! Not necessarily this exact number. This approximation would probably require you to do 10's of iteration (I can't be sure), but you can get "an" approximation using Simpson's rule that's close to the exact value of the integral. http://en.wikipedia.org/wiki/Simpson's_rule

Answer 21

lemme see if it works

Answer 22

http://www.youtube.com/watch?v=ns3k-Lz7qWU

Answer 23

http://www.youtube.com/watch?v=uc4xJsi99bk&feature=related

Answer 24

here f(a) = f(0) but that is the integration of that (tan^2/x^2+1) which is vry hard 2 evaluate

Answer 25

I don't understand what you mean.

Answer 26

We're using a numerical method because we are unable to evaluate this integral, this is the whole point.

Answer 27

yeah im trying to use the simpsons rule so wen i subsitute into it i get the expression
1/6 [ f(a)+ 4(1/2) + 1/2)] and istn f(a) taht integral

Answer 28

i got the fromula from wikepedia

Answer 29

No, the formula is considering f(x)=tan^2(x)/(1+x^2). make sense?

Answer 30

not really

Answer 31

Look closer at the formula :)

Answer 32

You have f(x)=tan^2(x)/(1+x^2), a=0, and b=1. You have everything you need. For instance, f(0)=tan^2(0)/(1+0)=0.

Answer 33

ohhhhhhhhh XD......

Answer 34

I have to go in a few minutes, I think you will do fine.

Answer 35

Yes i get it now! THANK YOU

Answer 36

Glad to help! :)