## onegirl Group Title Find the function f(x) satisfying the given conditions. (HINT: You are finding the value of C) one year ago one year ago

1. onegirl Group Title

2. myininaya Group Title

Find $\int\limits_{}^{}f'(x) dx=f(x)+C, \text{ where } (f)'=f'$

3. myininaya Group Title

Or evaluate

4. myininaya Group Title

Integrate the function given to get from f' to f.

5. myininaya Group Title

Don't forget when you integrate, put +C.

6. onegirl Group Title

can u explain? :/

7. myininaya Group Title

$\int\limits_{}^{}f'(x) dx=\int\limits_{}^{}(4x^2-1) dx$ You may find it easy to use the following: $\int\limits_{}^{}x^n dx =\frac{x^{n+1}}{n+1}+C, n \neq -1$ This is because $(\frac{x^{n+1}}{n+1})'=(n+1) \cdot \frac{x^{n+1-1}}{n+1}=x^{n+1-1}=x^n$ And you may also want to use $\int\limits_{}^{}k dx=kx+C \text{ where} K, C \text{ are a constant}$

8. myininaya Group Title

This is because (kx+C)'=(kx)'+(C)'=k(x)'+0+k(x)'=k(1)=k

9. onegirl Group Title

okay thanks

10. zepdrix Group Title

Are you familiar with the idea of Integration yet? Or has it only been introduced to you as the process of finding the anti-derivative so far?

11. onegirl Group Title

no i'm not familiar

12. onegirl Group Title

@Best_Mathematician can u help?

13. Loser66 Group Title

|dw:1367625325100:dw|

14. Loser66 Group Title

so, when you have f' (4x^2 +1) take integral to get back the original function. . when take integral, the solution for that method always a family solution. in case they give you the special solution, that means they want you to pick out just special C in set of family solution . take integral of f' you have f(x) = 4x^3/3 -x +C and when they give you f(0) =2 just plug 0 into the function you' ve just got. to find C f(0) = 4 *0^3/3 -0 +C = 2 ---> C =2 that's it

15. onegirl Group Title

ohhh okay

16. Loser66 Group Title

sorry , one more step. plug C back to f(x) = 4x^3/3 - x +2

17. Loser66 Group Title

I 'm supper dummy at teaching, hope you can understand what i mean

18. onegirl Group Title

so plugging 2 back into f(x) = 4x^3/3 - x + 2 right?

19. Loser66 Group Title

yep

20. onegirl Group Title

okay

21. onegirl Group Title

i got 32/3 or 10.6666

22. Loser66 Group Title

hey, you misunderstand the concept, they ask you to find out C, and you got C =2 that's it. just plug C =2 into the function, nothing to do more.

23. onegirl Group Title