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

1. jennychan12

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

2. jennychan12

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

3. Argos

jenny you are a liar i think

4. jennychan12

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

5. Argos

becos that problem required fresnal integral

6. jennychan12

what?

7. wio

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

8. Argos

u can use u sub on that

9. jennychan12

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

10. jennychan12

if u = x^2 then du = 2xdx

11. Argos

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

12. jennychan12

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

13. Argos

so ur on u-sub section of the book?

14. jennychan12

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

15. igotzbeard

thats the way it is

16. igotzbeard

not an exponent

17. jennychan12

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

18. wio

This isn't a candidate for u sub.

19. igotzbeard

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

20. igotzbeard

no place to apply a substitution

21. wio

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

22. k.rajabhishek

|dw:1357267172296:dw|

23. jennychan12

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

24. LogicalApple

whats the name of the textbook

25. jennychan12

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

26. jennychan12

stewart

27. LogicalApple

7th edition?

28. jennychan12

5th

29. LogicalApple

which chapter section?

30. jennychan12

chapter 5 review #49

31. Argos

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

fresnal function is introduced in section 5.3

33. igotzbeard

lol wolframalpha? xD

34. jennychan12

haha same 5.3 is fundemental theorum

35. Argos

go to 5.3 examlpe number 3

36. jennychan12

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

37. Argos

thats illegail

38. Argos

but u gonna have to look up fresnal function elsewhere then

39. jennychan12

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

40. LogicalApple

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

wait let me rewrite that

42. LogicalApple

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

43. LogicalApple

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

44. wio

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

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

46. LogicalApple

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

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

48. LogicalApple

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

49. jennychan12

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

50. LogicalApple

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

51. jennychan12

thanks :)

52. wio

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

53. jennychan12

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

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

55. wio

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

56. LogicalApple

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.