Question

integrating from sinx to 1 (t^2 f(t)dt=1-sinx for all xE R ,then f(1/sq.root(3))

Answer 1

Try using the Equation button in the bottom.

Answer 2

Is it
\[\int\limits_{\sin x}^{1}t^2f(t) dt=1-\sin x?\]

Answer 3

Are you there?

Answer 4

Just tell me if what I wrote there is what you're asking about :)

Answer 5

yaa

Answer 6

Good. Do you know the fundamental theorem of calculus?

Answer 7

i dunn mayb

Answer 8

Hmm. I will start by taking the derivative of both sides. Taking the derivative of the integral can be done using:
\[\int\limits_{a}^{g(x)}f(t)dt=f(g(x)).g'(x)\]

Answer 9

Sorry write before the integral d/dx

Answer 10

but y

Answer 11

oh i gotta

Answer 12

\[{d \over dx}\int\limits_{\sin x}^{1}t^2f(t)dt={d \over dx}(1-\sin x)\]

Answer 13

You are leaving?

Answer 14

no

Answer 15

You got the formula I wrote above?

Answer 16

yaa but then with this we hav to find f(\[ 1/\sqrt{3}\])

Answer 17

I know.. We have to find f(x) first.

Answer 18

oh

Answer 19

It will take just two more steps.

Answer 20

k

Answer 21

\[\implies -(\sin^2 x)f(\sin x)\cos x=-\cos x \implies \cos x(- \sin^2 x f(\sin x)+1)=0\]

Answer 22

It follows that:
cos x=0 or
\[\sin^2 x f(\sin x)=1 \implies f(\sin x)={1 \over \sin^2 x}\]

Answer 23

Now to find the value of f(1/sqrt(3)).. put x=pi/3

Answer 24

k

Answer 25

Sorry.. not pi/3, just substitute x=sin^-1(1/sqrt(3))you will get:

Answer 26

bot acc to formula g(x) =1 then y we substitute sinx

Answer 27

\[f(\sin(\sin^{-1}(1/\sqrt3))=f(1/\sqrt3)={1 \over \sin^2(\sin^{-1}{1\over \sqrt3})}={1 \over 1/3}=3\]

Answer 28

Do you have the answer?

Answer 29

you know that sin(arcsinx)=x, right? because arcsin just "undoes" the sin since it's its inverse.

Answer 30

3

Answer 31

Ok.. that's what I got and showed above. I hope the steps are clear, and make sense to you.

Answer 32

thnks

Answer 33

r u teacher

Answer 34

No. I am a student.

Answer 35

quit intelligent

Answer 36

Thanks!! :)

Answer 37

passed out 12 this yr

Answer 38

What?

Answer 39

hav u passed out 12 this yr?

Answer 40

hav u passed out 12 this yr?

Answer 41

I don't know what that means.