## hba 2 years ago A particle moves along x-axis.It starts from rest at origin O and its acceleration after t sec is given by a=3-t . Calculate the displacment from O when it is at rest.

1. hba

@saifoo.khan

2. hba

Can you do it ?

3. jennychan12

find antiderivative twice for a = 3-t

4. saifoo.khan

integrate. a=3-t v = 3t - t^2/2 + C Now set it equal to zero to get time. Then integrate again, find the disp.

5. hba

Therefore, the answer is 18. Something which appeared in the (NUST) test.

6. hba

@saifoo.khan

7. saifoo.khan

REALLY? O_O

8. hba

Yeah

9. saifoo.khan

An O'levels student who have Add math can solve this too! D: D: D:

10. hba

Hmm,good :)

11. hba

What about hyperbolic functions ? You've done that ?

12. saifoo.khan

give me the problem, then i can tlel.

13. hba

$\int\limits_{}^{}e^x[\sinh^{-1} x+\frac{ 1 }{ \sqrt{1+x^2} }]dx=$

14. hba

@saifoo.khan Like this.

15. saifoo.khan

INtegration by parts?

16. saifoo.khan

idk how to deal with sinh^-1

17. hba

So you don't know hyperbolic functions ?

18. experimentX

use e^x(f(x) + f'(x)) rule differentiation of arcsinh(x) = 1/sqrt(...)

19. saifoo.khan

I guess no, then. :S

20. hba

hmm No need to worry about that it's easy,you can do that later. What about finding the area from a diag ?

21. saifoo.khan

We have to learn that parallelogram thing. But i can find the area/vol of a curve and stuff

22. hba

Lets see. find the Area A+B |dw:1356722864399:dw|

23. saifoo.khan

NOOO! Give me more difficult one.

24. hba

Ok.

25. hba

find the area A |dw:1356723204131:dw|

26. saifoo.khan

|dw:1356723438919:dw|

27. saifoo.khan

Let me grab a pen and paper.

28. hba

Hmm :)

29. saifoo.khan

Is calc allowed?

30. hba

No not allowed+You changed the question lol :P

31. saifoo.khan

Sinx graph starts from zero. lol.

32. hba

Oh okay then :/

33. saifoo.khan

Haha.

34. hba

Now solve it .

35. saifoo.khan

isk what's sin(pi/4). i can only solve with the help of calc.

36. hba

180/4

37. saifoo.khan

area under cos is 1/sqrt2

38. hba

Sin45=0.707

39. saifoo.khan

0.707-0.293 ?

40. hba

@saifoo.khan Solve it and let me know :)

41. saifoo.khan

0.414

42. hba

Don't do it in decimals.

43. saifoo.khan

dang.

44. saifoo.khan

1/sqrt2 - (-1+sqrt2)/sqrt2

45. saifoo.khan

Making: (2-sqrt2)/sqrt2

46. saifoo.khan

Making: $\frac{2\sqrt2-2}{2}$

47. saifoo.khan

48. hba

$\sqrt{2}-1 \ sq.unit$ Yeah right :D

49. saifoo.khan

Wheo! B)

50. hba

One more. Find the area enclosed by x=y^2 and y=x-2

51. saifoo.khan

umm okay. solving.

52. hba

k.

53. saifoo.khan

1,4

54. saifoo.khan

area under line = 2 squnits

55. saifoo.khan

trying to figure out about x=y^2

56. saifoo.khan

57. hba

Let me give you options lol A)9/2 sq.units B)9/4 // C)9/7 // D)7/9 // E)4/9 //

58. saifoo.khan

Can't fig out.

59. hba

I also couldn't figure this out lol :P

60. hba

@hartnn Can you solve it ?

61. hba

Find the area enclosed by x=y^2 and y=x-2

62. hartnn

this is double integration problem.. right ?

63. hba

i don't think so.

64. hartnn

plot both curves..

65. saifoo.khan

|dw:1356725537575:dw|

66. hba

@hartnn Yes ?

67. hartnn

sorry, got disconnected.

68. hartnn

|dw:1356727367179:dw| $$\int \limits_{y_1}^{y_2}f_1(x)-f_2(x)=\int \limits_{y_1}^{y_2}(y+2)-y^2dy|dw:1356727499321:dw|$$

69. hartnn

$$\int \limits_{y_1}^{y_2}f_1(x)-f_2(x)=\int \limits_{y_1}^{y_2}(y+2)-y^2dy$$

70. hartnn

find y2 and solve the integral

71. hartnn

sorry, y1 and y2 limits should be |dw:1356727654740:dw|