Question

James?

Answer 1

give me edals

Answer 2

so the answer is?

Answer 3

oh that was annoying i cldnt type

Answer 4

give me medals free medals for everyone

Answer 5

can you write the equation again please :D

Answer 6

\[ \frac{d \ }{dx} \int_{17}^x \sin(t^2)/t \ dt \]

Answer 7

d/dx(sinx^2/x) - d/dx(sin(17)/17)

Answer 8

No

Answer 9

where did i go wrong?

Answer 10

look at the earlier example with ln

Answer 11

k i will

Answer 12

wasn't it d/dx(F(x)-F(17))

Answer 13

oh i see where i went wrong!!!!

Answer 14

Yes, but F is not the integrand.

Answer 15

F(x)=-cosx/x???

Answer 16

Nooo

Answer 17

K just tell me the answer

Answer 18

Look at the ln example again.

Answer 19

In the example we subsituted t for x

Answer 20

In the example we subsituted t for x

Answer 21

\[ \frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt \]

Answer 22

What is the value of that expression?

Answer 23

i dont know i am feeling very stupid!!!!!!
dF/dx=ln(x^2+1)

Answer 24

If \[ F(t) = \int \ln(t^2+1) \ dt \] then
\[ \int_2^x \ln(t^2+1) \ dt = F(x) - F(2) \].

Hence
\[\frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt = \frac{d \ }{dx} (F(x) - F(2)) \]

Answer 25

righ

Answer 26

and by the Fund Theorem of Calculus, dF/dx = ln(x^2 + 1).
Also (d/dx)F(2) = 0 because F(2) is a number, a constant.

Hence the entire expression is just ln(x^2+1)

Answer 27

James do you think you help me please?

Answer 28

So, return now to the next example where the integrand has a sin function. What is the value of that derivative?

Answer 29

@mft, I'll try and get to it. unfortunately you're not the first to ask.

Answer 30

dont take james away form me:(

Answer 31

i can wait

Answer 32

quick rld613. I want to move on with you to yet another example afterwards

Answer 33

rld said she didn't need OS anymore

Answer 34

so (d/dx) int_17^x sin(t^2)/t dt = ...

Answer 35

i didnt get that why is 17 to th epower of x

Answer 36

\[ (d/dx) \int_{17}^x \sin(t^2)/t \ dt \]

Answer 37

yes

Answer 38

evaluate. What is the that equal to.

Answer 39

y is it wrong what i showed u b4?

Answer 40

plz be nice to me and show me all the step? :D

Answer 41

No. You write out the steps, following line by the line the example we just used for ln. I'm going to help someone else for a while and expect the right answer when I get back ;-)

Answer 42

LOL see u later :D

Answer 43

I'm serious. And I'll be back in 5 minutes, so hurry.

Answer 44

??

Answer 45

u did u come back already!!!

Answer 46

What's the answer?

Answer 47

K can u walk me thru the steps cuz like i bever learnt this stuff?
YOu r so scary LOL

Answer 48

I was hoping i wld have the answer b4 u wld return

Answer 49

teh answer wld sinx/x?

Answer 50

Exactly as before, exactly, let
\[ F(t) = \int \sin(t^2)/t \ dt \]
Then \[ \int_{17}^x \sin(t^2)/t \ dt = F(x) - F(17) \]
Thus the derivative of this definite integral
\[ \frac{d\ }{dx} (F(x) - F(17)) = ... \]

Answer 51

iSo what is F(x)?????

Answer 52

That is where i am going wrong

Answer 53

oh i know si(x)?

Answer 54

d/dx(si(x)?

Answer 55

like we've seen, we actually don't need an explicit formula for F(x). We just need to know it is this integral and then use the Fundamental Theorem of Calculus.

Answer 56

What is dF/dx here? What is it equal to?

Answer 57

By the FTC, dF/dx = .... what?

Answer 58

You are forsure ready to kill me!!!!!!!!!!!!!!!

Answer 59

You are forsure ready to kill me!!!!!!!!!!!!!!!

Answer 60

shakes head

Answer 61

dF/dx= sinx^2/x

Answer 62

correct. Hence the derivative wrt (with respect to) x of the entire integral equals what?

Answer 63

hey james can you help me with math?

Answer 64

This thing ... what's it equal to?

Answer 65

sinx^2/x????? this is a guess

Answer 66

it shouldn't be guess. it is exactly right.

Answer 67

oh ya !!!!!!!!

Answer 68

That is what i thought in the first place but i left out by accident the squared

Answer 69

I can be so annoying sometimes

Answer 70

Now one more to make sure you really understand.

Evaluate this:
\[ \frac{d \ }{dx} \int_x^{x^2} \sqrt{t^3+1} \ dt \]

Answer 71

oh u r so funny!!!

Answer 72

Now write out the steps. This problem isn't exactly the same as the others.

Answer 73

ok give me a sec

Answer 74

\[d/dx=(\sqrt{x ^{6}+1}-\sqrt{x ^{3}+1})\]

Answer 75

This one i guessed

Answer 76

I think it was suppossed to be dF/dx

Answer 77

The expression is equal to
\[ \frac{d \ }{dx} \left( F(x^2) - F(x) \right) \ \ \ \ \ \ --(*)\]
where by the Fund Theorem of Calculus, \[ dF/dx = \sqrt{x^3+1} \]
Now given that, evaluate the first expression, (*).

Answer 78

hint: you need to use the chain rule.

Answer 79

ok so let me try that

Answer 80

james u gotta help me out on this one

Answer 81

you think about it for a bit and write the answer sometime in the next day when you know what's going on.

Answer 82

alrighty thanks james

Answer 83

I will call you back when i get the

Answer 84

I got the answer :D

Answer 85

\[2x \sqrt{x ^{6}+1} - \sqrt{x ^{3}+1}\]
Here is my answer.
Thanks james for your help. I really appreciate it

Answer 86

that's it. Good

Answer 87

One more variation they might throw at you in the exam. Evaluate:
\[ \frac{d^2 \ }{dx^2} \int_2^x \ln(\cos t) \ dt \]

Answer 88

Oh this is very simple there is just one small catch that you have to differentiate it twice

Answer 89

d/dx(ln(cosx))
(1/cosx)*-sin(x)= -sin(x)/cos(x)
-tan(x)

Answer 90

exactly, good.

Answer 91

I think that is the answer. I took my final exam already and it was basically simple except ofr a related rates problem. Going on vacation for a month So see u then. Thanks for your help james

Answer 92

oh u are here LOL

Answer 93

Thanks for helping me out

Answer 94

sure. have a good vacation.

Answer 95

U better take a vacation from OS tooo!!! :D

Answer 96

I might just do that.

Answer 97

Ya u need a break to refresh again