Integral help again

Question

Integral help again

anonymous · Answer

can someone solve any problem from no 12?

anonymous · Answer

and 12 at the end also?

anonymous · Answer

$$f(1)=0$$

anonymous · Answer

$$\int_1^1 f(t)dt = 0$$

anonymous · Answer

$$f'(x)=\sqrt{1+2x}$$because the derivative of the integral is the integrand

anonymous · Answer

$$f'(4)=\sqrt{9}=3$$

anonymous · Answer

cause that is what you get when you  replace x by 4

anonymous · Answer

is the last one 
$$f'(x^2)$$?

anonymous · Answer

yes

anonymous · Answer

in C how di you replace t?

anonymous · Answer

ok $$f(x)=\int_1^x f(t)dt$$ so $$f(x^2)=\int_1^{x^2} f(t)dt$$

anonymous · Answer

in C?  
$$f'(x)=\sqrt{1+2x}$$ yes?

anonymous · Answer

so you replace t with the x value right? I got it

anonymous · Answer

exactly

anonymous · Answer

k last one

anonymous · Answer

$$f(x)^2=\int_1^{x^2}\sqrt{1+2t}dt$$

anonymous · Answer

that should have  been $$f(x^2)$$

myininaya · Answer

attachment

anonymous · Answer

now you take the derivative using the chain rule

anonymous · Answer

derivative of "outside function" evaluated at "inside function" times derivative of "inside function"

anonymous · Answer

here "outside" is the integral, "inside" is x^2

anonymous · Answer

$$\frac{d}{dx}\int_1^{x^2} \sqrt{1+2t} dt=\sqrt{1+2x^2} \times 2x$$\]

anonymous · Answer

i replaces t by x^2 and then multiplied at the end

anonymous · Answer

got it.

anonymous · Answer

good!

anonymous · Answer

Well, I did 10 by myself but can you check my answer A=6, B=-2.5 C=.5

anonymous · Answer

hello myininaya!

myininaya · Answer

someone said they could not open my file earlier
can someone give it a try to see if it still doesn't open?
hey satellitle

anonymous · Answer

which file?

anonymous · Answer

cheater.  where is the latex?

anonymous · Answer

i will try but i can barely read them

myininaya · Answer

ravsau scroll up the file should be there

anonymous · Answer

A it's 0 to 3 B; 2 to 5 C; 7 to 3

anonymous · Answer

ok the idea is you take the anti derivative, put the +C replace x by 2 and set the result = 1 to solve for C

anonymous · Answer

dont you just count the triangles? because integrals = area? something like that?

anonymous · Answer

first is $$\frac{-1}{x}+\frac{x^2}{2}+C$$

anonymous · Answer

#10?

myininaya · Answer

i think he is talking about the second 10

anonymous · Answer

hey myininaya i could open your file . Thanks for your effort

anonymous · Answer

the second ten?

anonymous · Answer

second 10 yes.graphing one

myininaya · Answer

yes just use areas to find the areas or net areas under the curve

myininaya · Answer

areas of triangles*

anonymous · Answer

mininaya can you do  it?  i am old and tired and my eyes hurt

myininaya · Answer

this is some really bad lag for me
i don't know how much longer i can stay and let this lag lag me

anonymous · Answer

plus i need to go get my beauty rest

myininaya · Answer

satellite wants to do it 
i don't want to take his thunder

anonymous · Answer

actually this is all jumping around.  area of rectangle and triangles. i guess i can try it

anonymous · Answer

cool

anonymous · Answer

i get 6.5 for the first one

anonymous · Answer

from 2 to 5 looks like 0

myininaya · Answer

(1)1+3*1*1/2+4*2*1/2=1+3/2+4=5+3/2+13/2
gj on the first one

anonymous · Answer

yes especially since i eyeballed it

anonymous · Answer

how bout the second?

myininaya · Answer

those two triangles have the same area except one is above the x-axis and one is below so the net area is 0

anonymous · Answer

i get 1/2 for the last one

myininaya · Answer

7 to 3?
or 
3 to 7?

myininaya · Answer

ok 7 to 3

anonymous · Answer

last one 7 to 3

anonymous · Answer

so A was 6.5? B was 0 c half?

myininaya · Answer

yes i get the same 
if we look from 3 to 7 we have
-1/2*1*2+(-1/2*1*1)+1/2*2*1=-1/2
so from 7 to 3 we have 1/2 
gj satellite

anonymous · Answer

that is what i got.  but my eyes are off tonight and this thing is jumping around like crazy. i will wait for my learned colleague to reply

anonymous · Answer

amistre made it to 1000 today!

anonymous · Answer

i was so chuffed with myself for giving him his 1000 th medal

myininaya · Answer

he said he will let me have his bike and not you

anonymous · Answer

can i ring the bell at least?

myininaya · Answer

no!

anonymous · Answer

find my post and condulate him

anonymous · Answer

:(

anonymous · Answer

k thanks guys.

anonymous · Answer

http://openstudy.com/users/satellite73#/users/satellite73/updates/4de530c34c0e8b0bc89bb0d8

anonymous · Answer

gnight all

myininaya · Answer

lol 
its for you own good
if you ring the bell you will get too attached
later ravsau

anonymous · Answer

grrrr

myininaya · Answer

nite satellite 
you can ring the bell once

anonymous · Answer

thanks that is very generous of you.