## AravindG Group Title Find the points of maxima/minima of 2 years ago 2 years ago

1. hal_stirrup Group Title

whats you Q?

2. AravindG Group Title

$\int\limits^{x^2}_0 [(t^2-5t+4)/(2+e^t)]dt$

3. AravindG Group Title

@amistre64 , @UnkleRhaukus , @Callisto , @Ishaan94

4. AravindG Group Title

@.Sam.

5. AravindG Group Title

@cwrw238

6. UnkleRhaukus Group Title

(t2−5t+4)=(t-1)(t-4)

7. hal_stirrup Group Title

am not sure if you need to know the answer or how to go about answering the question.

8. AravindG Group Title

?

9. AravindG Group Title

help pls

10. hal_stirrup Group Title

so i can help. i need to know what are you really looking for?

11. AravindG Group Title

maxima and minima !!

12. cwrw238 Group Title

the expression in the integral = 0 for max/minm points ( i think) isn't that right guys?

13. Spacelimbus Group Title

I would have guessed so @cwrw238, I am not sure if the integrated function and the to be integrated function share similarities in minima and maxima though. but for linear functions that seems to be the case (-:

14. cwrw238 Group Title

so (t - 4)(t - 1) = 0 t = 4 or 1 so you have turning points at values t = 4 and t = 1 second derivative is 2t - 5 when t = 4 this is positive so t=4 is a minimum when t = 1 this is negative so t = 1 is a maximum

15. cwrw238 Group Title

yea spacelimbus - im not sure either!

16. hal_stirrup Group Title

integral (4-5 t+t^2)/(2+e^t) dt = (5/2-t) Li_2(-e^t/2)+Li_3(-e^t/2)+t^3/6-(5 t^2)/4-1/2 t^2 log(1/2 (e^t+2))+2 t+5/2 t log(1/2 (e^t+2))-2 log(e^t+2)+constant

17. Spacelimbus Group Title

THe polylogarithmic function behaves weirdly for min/max though @hal_stirrup , I wouldn't know how to solve that expression for zeros.

18. Spacelimbus Group Title

@cwrw238, lets think about this together, an integral is the antiderivative of a function right? And to find minima and maxima you need to set the derivative to zero, correct?

19. hal_stirrup Group Title

yes

20. Spacelimbus Group Title

therefore, what we have next to the integral expression is the derivative of the function, I would say your answer is pretty much correct.

21. Spacelimbus Group Title

is the derivative of the integrated function*

22. cwrw238 Group Title

makes sense to me -though i'm learning calculus at present time so I'm not expert by any means

23. cwrw238 Group Title

thats some integral!!!! lol

24. hal_stirrup Group Title

ok integral is the area under the curve.

25. cwrw238 Group Title

yes

26. Spacelimbus Group Title

Oh okay @cwrw238, I believe it's correct, it's how I would read it anyway, it's basically an easier way (that looks more complicated at first glance though) If you integrate an arbitary function you get F(x), if you derive that again you get f(x), the derivative of a function is what decides if there are minima and/or maxima points present. So in our case, just the f(x) =0, because that is the derivative of the obscure function I wouldn't know how to integrate without series and transformations *grins*

27. cwrw238 Group Title

nor me!! - yes i think these values of t correspond to max ./ mini on the graph . just noticed the limits on integral - i expect that t^2 not x^2

28. Spacelimbus Group Title

Seems to be a time -> position transformation, but I cannot tell, however, the points we have found are extremal points, but to decide wether they are min/max or not we need the second derivative of the function f(x) which is a bit more complicated since it requires the use of the quotient rule.

29. hal_stirrup Group Title

typo error cwrw238 i think too.

30. cwrw238 Group Title

oh yes of course - i only differentiated the numerator!!! my mistake there.

31. cwrw238 Group Title

typo?

32. Spacelimbus Group Title

not a big thing, just some additional work (-: but @AravindG can verify these points for himself.

33. cwrw238 Group Title

i just entered the integral on wolfram alpha http://www.wolframalpha.com/input/?i=integrate+++%28t%5E2−5t%2B4%29%2F%282%2Be%5Et%29+ - theres no min/max on the plot at the points t = 1 and 4 so it looks like i'm wrong...

34. hal_stirrup Group Title

ok i recommend 1: to go back the question and se if there is a typo error. 2: go back to basic integration methods in definite integral . and you will be able to solve it .

35. hal_stirrup Group Title

example :$\int\limits_{}^{} x^4$ its primative funaction is : $x ^{5}/5$