Suppose f, f', f", are continuous on [0, ln2] and that f(0) = 0, f'(0) = 3, f(ln2) = 6, f'(ln2) = 4 and the integral of (e^-2x * f(x) dx from 0 to ln 2) = 3.

Find the vlaue of the integral of (e^-2x *f"(x) dx) from 0 to ln 2.

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- May 30th 2006, 01:46 PMSusie38Another homework problem: Calculus
Suppose f, f', f", are continuous on [0, ln2] and that f(0) = 0, f'(0) = 3, f(ln2) = 6, f'(ln2) = 4 and the integral of (e^-2x * f(x) dx from 0 to ln 2) = 3.

Find the vlaue of the integral of (e^-2x *f"(x) dx) from 0 to ln 2. - May 30th 2006, 05:11 PMSoroban
Hello, Susie!

Quote:

Suppose are continuous on

and that

and:

Find the value of:

. . Let:

. . Then:

And we have:

Do by-parts again:

Let:

Then:

So we have:

and:

Now we evaluate from to

. . Note that:

We have:

. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .

Hence: . .

. . . . . . .

But someone check my work . . .*please!* - May 30th 2006, 05:20 PMmalaygoelQuote:

Originally Posted by**Soroban**

- May 30th 2006, 05:22 PMmalaygoelQuote:

Originally Posted by**malaygoel**

- May 30th 2006, 06:27 PMSoroban
Hello, malaygoel!

Quote:

I think that you have substituted but forgot to substitute

- May 31st 2006, 09:46 AMmalaygoelQuote:

Originally Posted by**Soroban**

- Jun 3rd 2006, 03:10 PMNichelle14
how did you get 16- 3/4? I got 16 - 3.

Can you explain your answer? - Jun 3rd 2006, 05:25 PMmalaygoelQuote:

Originally Posted by**Soroban**

and got the answer 16

can you follow upto here

if we substitute 0 we will get 1/3

result of integration is difference of the resulting function at upper limit and lower limit

tell me if I am not clear to you - Jun 3rd 2006, 05:39 PMNichelle14
sorry I don't see how still.

- Jun 4th 2006, 06:56 AMmalaygoelQuote:

Originally Posted by**Nichelle14**

explain me how you got 3. - Jun 4th 2006, 08:25 AMNichelle14
I substituted 0 in for x, this is after substituting the ln 2

-(e^-2(0)f'(0) + 2e^-2(0)f(0))

-(1(3) + 2(1)(0)) = -3 - Jun 4th 2006, 09:46 AMmalaygoelQuote:

Originally Posted by**Nichelle14**

I was wrong

it is 16 -3 =13 :rolleyes: