## jennychan12 Group Title Find an antiderivative F of f(x) = x^2*sin(x^2) such that F(1) = 0. one year ago one year ago

1. jennychan12 Group Title

I don't think you can use u-sub here. cuz then it'd be f(u) = u*sinu..

2. jennychan12 Group Title

and i haven't learned trig sub or integration by parts yet.

3. Argos Group Title

jenny you are a liar i think

4. jennychan12 Group Title

-_- i haven't. but i can do integration by parts. but my teacher never taught it.

5. Argos Group Title

becos that problem required fresnal integral

6. jennychan12 Group Title

what?

7. wio Group Title

Use $$u = x^2$$. Then $$x = \sqrt{u}$$

8. Argos Group Title

u can use u sub on that

9. jennychan12 Group Title

$f(x) = x^2\sin(x^2)$

10. jennychan12 Group Title

if u = x^2 then du = 2xdx

11. Argos Group Title

well what method are you allowed to use if you can't use trig or parts

12. jennychan12 Group Title

that's what i don't understand. u-sub doesn't really work...

13. Argos Group Title

so ur on u-sub section of the book?

14. jennychan12 Group Title

no it's a review packet. i learned area, u-sub, trapezoid rule, and simpson's rule

15. igotzbeard Group Title

thats the way it is

16. igotzbeard Group Title

not an exponent

17. jennychan12 Group Title

no it's $f(x) = x^2\sin(x^2)$

18. wio Group Title

This isn't a candidate for u sub.

19. igotzbeard Group Title

u = x^2 du = 2x dx cant use u du sub

20. igotzbeard Group Title

no place to apply a substitution

21. wio Group Title

$\frac{1}{2}\int \sqrt{u}\sin(u)du$Isn't helpful.

22. k.rajabhishek Group Title

|dw:1357267172296:dw|

23. jennychan12 Group Title

-_- it was in the textbook in the chapter 5. we don't do trig sub/parts until chapter 8...

24. LogicalApple Group Title

whats the name of the textbook

25. jennychan12 Group Title

although i know how to do parts but my teacher never taught it.

26. jennychan12 Group Title

stewart

27. LogicalApple Group Title

7th edition?

28. jennychan12 Group Title

5th

29. LogicalApple Group Title

which chapter section?

30. jennychan12 Group Title

chapter 5 review #49

31. Argos Group Title

integral x^2 sin(x^2) dx = 1/4 (sqrt(2 pi) C(sqrt(2/pi) x)-2 x cos(x^2))+constant C(x) is the fresnal C integral Medal pls

32. Argos Group Title

fresnal function is introduced in section 5.3

33. igotzbeard Group Title

lol wolframalpha? xD

34. jennychan12 Group Title

haha same 5.3 is fundemental theorum

35. Argos Group Title

go to 5.3 examlpe number 3

36. jennychan12 Group Title

we don't use stewart. we use larson. my teacher just photocopied this from the stewart textbook

37. Argos Group Title

thats illegail

38. Argos Group Title

but u gonna have to look up fresnal function elsewhere then

39. jennychan12 Group Title

she owns like ten stewart textbooks. -_- i'll just use parts then...

40. LogicalApple Group Title

I guess one way to approach it is: $F(t) = \int\limits_{1}^{x} t ^{2} \sin(t ^{2})$ This way the integral evaluated at x = 1 results in 0, and its derivative is just the original function

41. LogicalApple Group Title

wait let me rewrite that

42. LogicalApple Group Title

$F(x) = \int\limits\limits_{1}^{x} t ^{2} \sin(t ^{2}) dt$

43. LogicalApple Group Title

That way when it is evaluated at F(1), you still get 0. And the derivative is the original function.

44. wio Group Title

If you used Simpson's rule or Midpoint rule on that, you'd get a nasty summation but it is within the rules.

45. jennychan12 Group Title

oh wow. thanks @LogicalApple that's the answer in the book -___-

46. LogicalApple Group Title

Well it makes sense, right? We don't actually have to take an integration. We know from the fundamental theorem of calculus (either part 1 or 2, i forget) that the derivative of F(x) here is just the inside of the integral evaluated at x. And for the limits of integration, we know that if we integrate from a to a we always get 0. So let a = 1, that way F(1) is an integral evaluated from 1 to 1.

47. jennychan12 Group Title

yes but i never thought of it that way... *sigh*

48. LogicalApple Group Title

Stewart doesn't mess around.. I'm in chapter 5 on the 7th edition.

49. jennychan12 Group Title

oh same here i think. my teacher uses both stewart and larson. we teach from larson.

50. LogicalApple Group Title

I will have to check that one out. Anyway good luck with your studies!

51. jennychan12 Group Title

thanks :)

52. wio Group Title

I think it's sort of an unfair question. Should have specified a bit more the rigor.

53. jennychan12 Group Title

same. my teacher likes stewart because they have "more pictures" and "good problems". which means that she puts them on quizzes and tests. :[

54. jennychan12 Group Title

i guess it just makes u think about the concept more?

55. wio Group Title

If they said something like "in terms of an indefinite integral" then it would have been fair.

56. LogicalApple Group Title

Yeah sometimes Stewart's questions are very very chapter-specific That's why I asked what chapter the problem was in to get an idea of the context of the question.