Differentiation/Intergration using exponential - Sorry to spam questions (1 Viewer)

[Lucas_]

Hi guys,

From my assigned work I have had two problem questions,




I proved that x^3e^x differentiated, was indeed the above integral. I'm not sure if the wording just wanted me to prove it or if it wanted me to solve the integral as well. What does 'determine' mean in a mathematical context?


Not going to lie, I have no idea how to show this. f(-x) confused me, is it just the function all bracketed with a minus sign, or all the x's are -x's and then I use a value to prove that they both = the same number?

Thanks + rep

 

[qwerty44]

For the first one, it just means using for first solution, determine the second one. They say determine because your not really solving as the integral your asked to find is the derivative of the first part, so the primitive function is x^3e^x + c.

 

[qwerty44]

For the second question, f(-x) just means to sub -x into x for that function.

So f(x)=1+e^x
and f(-x)=1+e^-x

 

[qwerty44]

 

[Carrotsticks]

Are you sure about that?

 

[Peeik]

(sorry a little off topic here) Does anyone know how to put pictures like the OP did in their post so that it is visible and wasnt a hyperlink? Mine keeps becoming a hyperlink

 

[RealiseNothing]

It doesn't equal 3.

 

[RealiseNothing]

 

[Carrotsticks]

(sorry a little off topic here) Does anyone know how to put pictures like the OP did in their post so that it is visible and wasnt a hyperlink? Mine keeps becoming a hyperlink

(IMG)Link to picture(/IMG)

But with square brackets []

 

[Lucas_]

Repped RealiseNothing for a great response

Can anybody be more clear on the first question? Does 'hence determine' mean solve the integral or just prove that it is the correct integral by differentiating the above equation?

 

[Timske]

Repped RealiseNothing for a great response

Can anybody be more clear on the first question? Does 'hence determine' mean solve the integral or just prove that it is the correct integral by differentiating the above equation?

Using the result of d/dx x^3e^x to integrate it

 

[qwerty44]

oh shit i multiplied e^x and e^-x....keep making that mistake

 

[qwerty44]

Repped RealiseNothing for a great response

Can anybody be more clear on the first question? Does 'hence determine' mean solve the integral or just prove that it is the correct integral by differentiating the above equation?

You don't have to solve anything. If you are told to derive f(x) and the answer is f'(x), then when told to integrate f'(x) the answer is f(x) + C.

 

[Lucas_]

Thank you everyone