## anonymous 4 years ago Can some please help me with this: Suppose f(3)=4, f(8)=8, f'(3)=2, f'(8)=9, and f'' is continuous. Find the value of the definite integral

1. anonymous

$\int\limits_{3}^{8}$ xf''(x)

2. anonymous

I need this broken down in layman terms

3. amistre64

well, if we try to use this according to the definition of integration .. what can we get?

4. amistre64

$f(x)=\int f'(x)dx$is the basic understanding of an integral

5. anonymous

I don't understand what to do with the function values

6. amistre64

it would appear to me that the 3 to 8 is the limits of integration

7. amistre64

$\int_{3}^{8}x\ f''(x) dx$ is what we have to work with and all we have to determine is what to do with the "x" part

8. amistre64

i might have to logout and back in to do this ...

9. anonymous

ok

10. amistre64

the math still aint processing from the latex on my end; you see normal equations on your end?

11. anonymous

yes I can see them.

12. amistre64

good :) well then, lets see if we can move ahead with this then i think we can apply integration by parts to this .. just a gut felling

13. amistre64

$\int u dv =uv-\int v du$

14. anonymous

ok so would i just use xf''(x) as my function to integrate?

15. amistre64

to wit: u = x v = f'(x) du = dx dv = f''(x) dx yes

16. anonymous

so when I integrate that is where the values that were given will be used?

17. amistre64

$\int xf''(x)=xf'(x)-\int f'(x)dx$ $\int xf''(x)=xf'(x)-f(x)$

18. amistre64

yes

19. amistre64

im sure that looks alot more inspiring on your end lol

20. anonymous

I shows up normal on my end

21. amistre64

(8 f'(8)) - f(8) ) - (3 f'(3)-f(3)) should be our results

22. anonymous

ok I didn't get that far but how did you get rid of the x?

23. amistre64

I didnt; i just used it in the integration by parts formula. there is no reason to get rid of it since the interval speaks in x to begin with

24. anonymous

ok i see know you used the limit that you are evaluating the integral?

25. amistre64

yep

26. anonymous

I got 53, is that correct?

27. anonymous

I see my error, I am about to recalculate it

28. amistre64

8*9 - 8 - (3*2-4) 72-8 - (6-4) 64 - 2 = 62

29. amistre64

i hope that makes more sense, I have to be heading out now. good luck :)

30. anonymous

I accidently used 8*8-9-)-(3*2-4). Thank you that was really helpful.