anonymous 4 years ago $\LARGE f'(x)=x^2+3x \;\; ,\;\; f(1)=5\;\;\;\;\Longrightarrow f(2)=?$ I need some hints

1. anonymous

f(x) can be obtained by integration........then use f(1) to find value of c, then find f(2)

2. anonymous

ya suroj ur correctt

3. anonymous

got it?

4. anonymous

$\LARGE f(x)=\frac13 x^3 +\frac32 x^2 \;\;\;\;??$

5. anonymous

you left +C at the end

6. anonymous

you need to add +C at end because it is integration

7. anonymous

indefinite integration

8. anonymous

ok but... I need to firnd f(2) then how??

9. anonymous

on the second condition when x=1, y=5, you see , put those values and get c

10. anonymous

$\LARGE \int\limits x^2+3x \;dx = \frac13 x^3+\frac32x^2+C$

11. anonymous

put the c back on f(x) and get complete f(x) equation and then find f(2)

12. anonymous

yes

13. anonymous

correct

14. anonymous

how can I know what the value of C is ??

15. anonymous

I see it you told me before... let me try, I'll see what I can do :D

16. anonymous

see second condition f(1) is 5 than mean when x=1 , y=5

17. anonymous

see f(x) is what you get by integration

18. anonymous

because you integrate f'(x)

19. anonymous

did you catch it?

20. anonymous

is C=19/6 ??

21. anonymous

I'm still dizzy ! O_O

22. anonymous

yes you got it

23. anonymous

now put that C back in f(x)

24. anonymous

got it?

25. anonymous

ahh yeah... now I'll do it thank you very much ;)

26. anonymous

no problem lol

27. anonymous

$f \left( x \right) = x ^{2} + 3x$ $f \left( 1 \right) = 1^{2} + 3 \times 1 = 5$ $f \left( 2 \right) = 2^{2} + 3 \times 2 = 10$ simple.

28. anonymous

@kreshnik another simple way to do something.

29. anonymous

@JoshDavoll WRONG... the answer IS $\frac{71}{6}$ !! Thanks for the help !

30. anonymous

hahaha... obviously , you mus be 10-12 years ... LOL