## anonymous 3 years ago find the integral.

1. anonymous

-5^-x/(log(5))+C

2. anonymous

|dw:1361280612277:dw|

3. anonymous

i have been trying to enter the site since yesterday did you all have the same problem?

4. anonymous

anyways there are many ways to solve this problem, one of them would be Taylor series the other one would be substitution method

5. anonymous

@mathsmind yea ive been having problems with it to so i did the problems i know how to do until it finally works

6. anonymous

@mathsmind i figured that one out im stuck on another one now

7. anonymous

evaluate the intergal |dw:1361284859202:dw|

8. anonymous

@mathsmind that one ^^^

9. anonymous

sorry i meant i was having problems entering the website since yesterday

10. anonymous

i know how to solve both integral in my head

11. anonymous

@mathsmind how long are you going to be one today ?

12. anonymous

it depends on my work, if i am busy or not

13. anonymous

14. anonymous

were you able to log on to the site

15. anonymous

@mathsmind which one ? lol

16. anonymous

oh no i wasnt i answered it above

17. anonymous

this website? openstudy

18. anonymous

19. anonymous

i felt like crying lol, with out this website i don't know what id do

20. anonymous

ok let me reply to the last integral

21. anonymous

the answer for the last integral would be pi/6

22. anonymous

now by looking at the last integral you can find out from the table that it is equal to arcsin(x/2)

23. anonymous

for the 4-x?

24. anonymous

$\int\limits_{0}^{1}\frac{ dx }{ \sqrt{4-x^2} }$

25. anonymous

is that the integral or not?

26. anonymous

yepp

27. anonymous

28. anonymous

how did you get it?

29. anonymous

ok there are two ways to do that

30. anonymous

one way is to look at the arctrigs integrals

31. anonymous

you know the table of integrals right!

32. anonymous

the other way is to go through full substitution method

33. anonymous

lol no but ill look them up

34. anonymous

ok do you want detailed solution then

35. anonymous

the u sub thing ?

36. anonymous

yep

37. anonymous

you let x=2u

38. anonymous

x^2 = 4u^2

39. anonymous

okay i get it so far

40. anonymous

can you differentiate the last bit?

41. anonymous

dx = 2du

42. anonymous

$\int\limits_{0}^{1}\frac{ 2du }{\sqrt{4-4u^2} }$

43. anonymous

$\int\limits\limits_{0}^{1}\frac{ du }{\sqrt{1-u^2} }$

44. anonymous

45. anonymous

thanks that was kind of you, and you are a bright student

46. anonymous

let me give you a third way how to do that

47. anonymous

i understand the u-sub the most

48. anonymous

i have three more integral questions

49. anonymous

ok go ahed

50. anonymous

you need to know different methods to solve one problem , that for future note...

51. anonymous

altho the differentiate part is a bit hard

52. anonymous

i have a phone call but still submit your work

53. anonymous

but ill look back it later because i have to get this course done to graduate

54. anonymous

no i meant you make y =2sinx sub

55. anonymous

different substitution

56. anonymous

if you look at the unit triangle you can figure out that you need a sin sub

57. anonymous

okay

58. anonymous

find the intergal |dw:1361286908472:dw|

59. anonymous

again you are going to get an arctan but now we need to look at the factors

60. anonymous

just by looking at this integral we will get 4/3arctan(3x) +c

61. anonymous

the question is what was x=? in this u sub

62. anonymous

you need to assume that 3x=u, 9x^2=u^2, 3dx=du

63. anonymous

$\int\limits \frac{ 4du }{ 3(1+u^2) }=\frac{ 4 }{ 3}\arctan(u)+c$

64. anonymous

$u=3x, \therefore \frac{ 4 }{ 3 }\arctan(3x)+c$

65. anonymous

66. anonymous

okay i just did the other one so i have one more integral question

67. anonymous

|dw:1361287534741:dw|

68. anonymous

ok

69. anonymous

again you can see we will get the arctan + something

70. anonymous

your answer should be$\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ 2}(x-1))+c$

71. anonymous

$\int\limits\limits\limits \frac{ dx }{4+(1-x)^2}$

72. anonymous

now 2u=1-x, 4u^2=(1-x)^2,

73. anonymous

now one thing you need to know is how to let the 4 be a one in the denominator

74. anonymous

how do i know that?

75. anonymous

ok let me show, it is clear from the u-sub

76. anonymous

remember that 2u =1-x, 2du=-dx

77. anonymous

okay so far so good lol

78. anonymous

$\int\limits\frac{ 2du }{4(1+(u)^2)}$

79. anonymous

can you see it better this way?

80. anonymous

$\frac{ 1 }{ 2 }\arctan(u)+c$

81. anonymous

$2u=1-x, \space u=\frac{ 1 }{ 2 }(1-x)$

82. anonymous

$\frac{ 1 }{ 2 }\arctan(\frac{ 1 }{ 2 }(1-x))+c$

83. anonymous

84. anonymous

okay thanks ! im working on some ill let you know if i need more help

85. anonymous

you don't sound like you got the last one?

86. anonymous

lol i havent fully looked at it yet im finishing a problem

87. anonymous

ok

88. anonymous

89. anonymous

lol yeahh i was wondering how you knew that,but im looking at it now

90. anonymous

i still don't understand how the engagement scheme works on open study

91. anonymous

i get that one

92. anonymous

good

93. anonymous

i think its by the questions you answer, and medals you receive

94. anonymous

95. anonymous

the one that has learner next to it

96. anonymous

lol i thinks its from asking questions cause thats how you learn right

97. anonymous

okay i found two i need help on

98. anonymous

99. anonymous

determine which of the integrals can be found using the basic integration formulas you have studied so far in the text.

100. anonymous

i think you need to open a new thread because this one is getting heavy with BW

101. anonymous

lol okay i will