Can anyone help me with a very difficult First year calculus problem?

[webnewland]

The problem is located at http://24.76.230.229/math.jpg

for f(0) I got rather quickly, but f(1) was very difficult.
The answer I got was sqr(75/13)

First i found out what the integral equal to, so i isolated the integral and got (5/f(x)) - 1

I took the derivitive of both side of the original equation, and substituting the integral with (5/f(x)) - 1

After that, I moved all the x and dx to one side and f(x) and df to the other side and used separable differential equation

and then plugging in x=0 to find out the C that came out of the integration and then plug in x=1 to find the final answer.

Can anyone check if I am doing it correctly and whether the answer is sqr(75/13)?

Thanks a lot in advance

 

[blueghost75]

doh.....I forgot how to do that already...

we just finished up for the year, and are going to be reviewing everything for the AP test...:Q

I recall having trouble with that particular section though.

Got any other not-so-hard Qs?

 

[webnewland]

heh, ya it's quite difficult. That is the only question I have right now, final is coming for me also and i'm not very confident right now

 

[blueghost75]

what is throwing me off is the f(t) and the f(x) on the right side of the equation.....that seems to make it recursive? i hate those....

i could be totaly off here.....

 

[webnewland]

it's not really recursive. The integral part was my teacher adding BIG difficulty to the question. so is the f(x) on both side

 

[blueghost75]

what type of calc course are you taking, out of curiosity?

i'm in high school AB calc.

 

[b0mbrman]

First step is:

f(1) = 5 - (t^2)(f(t))(dt)(integral(f(1)))

but that's where I don't want to think anymore