D.E. + Integration: Find Value of k

[zorro]

Homework Statement

Let [URL]http://203.196.176.41/VLEBT_RootRepository/Resources/b38e1b90-9ba0-45c6-a1eb-65288fa31b27.gif,[/URL] x > 0. If [URL]http://203.196.176.41/VLEBT_RootRepository/Resources/47280b1e-999e-44b0-a05e-5ad5243b0750.gif,[/URL] then one of the possible values of k is

1)16
2)63
3)64
4)15

The Attempt at a Solution

Do I have to integrate the first function to find out f(x)? I think that function is non-integrable.

 

[hikaru1221]

If you write the 2nd integral as: $$\int ^4 _1 \frac {3e^{sint^3}} {t} dt$$ and then let x = t³, you will see the way

 

[zorro]

I got it. But then there is no use of the first sentence, right?

 

[HallsofIvy]

"Fundamental Theorem of Calculus"! That first part is telling you that, in the second part, you are integrating the derivative of f.

 

[hikaru1221]

@Abdul Quadeer: Not sure what you meant

 

[HallsofIvy]

Once you make the substitution u= x^3 as hikaru1221 suggested, you will be integrating (df/du)du. What is that integral?