## Ephilo 2 years ago find the integral.

1. rosjua

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

2. Ephilo

|dw:1361280612277:dw|

3. mathsmind

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

4. mathsmind

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

5. Ephilo

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

6. Ephilo

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

7. Ephilo

evaluate the intergal |dw:1361284859202:dw|

8. Ephilo

@mathsmind that one ^^^

9. mathsmind

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

10. mathsmind

i know how to solve both integral in my head

11. Ephilo

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

12. mathsmind

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

13. mathsmind

14. mathsmind

were you able to log on to the site

15. Ephilo

@mathsmind which one ? lol

16. Ephilo

oh no i wasnt i answered it above

17. mathsmind

this website? openstudy

18. Ephilo

19. Ephilo

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

20. mathsmind

ok let me reply to the last integral

21. mathsmind

the answer for the last integral would be pi/6

22. mathsmind

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

23. Ephilo

for the 4-x?

24. mathsmind

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

25. mathsmind

is that the integral or not?

26. Ephilo

yepp

27. mathsmind

28. Ephilo

how did you get it?

29. mathsmind

ok there are two ways to do that

30. mathsmind

one way is to look at the arctrigs integrals

31. mathsmind

you know the table of integrals right!

32. mathsmind

the other way is to go through full substitution method

33. Ephilo

lol no but ill look them up

34. mathsmind

ok do you want detailed solution then

35. Ephilo

the u sub thing ?

36. mathsmind

yep

37. mathsmind

you let x=2u

38. mathsmind

x^2 = 4u^2

39. Ephilo

okay i get it so far

40. mathsmind

can you differentiate the last bit?

41. mathsmind

dx = 2du

42. mathsmind

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

43. mathsmind

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

44. Ephilo

45. mathsmind

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

46. mathsmind

let me give you a third way how to do that

47. Ephilo

i understand the u-sub the most

48. Ephilo

i have three more integral questions

49. mathsmind

ok go ahed

50. mathsmind

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

51. Ephilo

altho the differentiate part is a bit hard

52. mathsmind

i have a phone call but still submit your work

53. Ephilo

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

54. mathsmind

no i meant you make y =2sinx sub

55. mathsmind

different substitution

56. mathsmind

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

57. Ephilo

okay

58. Ephilo

find the intergal |dw:1361286908472:dw|

59. mathsmind

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

60. mathsmind

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

61. mathsmind

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

62. mathsmind

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

63. mathsmind

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

64. mathsmind

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

65. mathsmind

66. Ephilo

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

67. Ephilo

|dw:1361287534741:dw|

68. mathsmind

ok

69. mathsmind

again you can see we will get the arctan + something

70. mathsmind

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

71. mathsmind

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

72. mathsmind

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

73. mathsmind

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

74. Ephilo

how do i know that?

75. mathsmind

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

76. mathsmind

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

77. Ephilo

okay so far so good lol

78. mathsmind

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

79. mathsmind

can you see it better this way?

80. mathsmind

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

81. mathsmind

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

82. mathsmind

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

83. mathsmind

84. Ephilo

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

85. mathsmind

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

86. Ephilo

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

87. mathsmind

ok

88. mathsmind

89. Ephilo

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

90. mathsmind

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

91. Ephilo

i get that one

92. mathsmind

good

93. Ephilo

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

94. mathsmind

95. mathsmind

the one that has learner next to it

96. Ephilo

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

97. Ephilo

okay i found two i need help on

98. mathsmind

99. Ephilo

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

100. mathsmind

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

101. Ephilo

lol okay i will