Integral Problem - Tibi01

[tiberiuiurco]

Hello guys. I've encountered a problem on the internet and i can't think of a solution for this ecuation. I just can't figure out the answer. Hope you can help me ^^ , please.
This is the image with the exercise:
I can't figure out a) and c)
At b) you just gotta derivate the F(x) and write the table of variation of the function. Seems easy. But the other ones.. idk
Much appreciated.

 

[Dr.Peterson]

Hello guys. I've encountered a problem on the internet and i can't think of a solution for this ecuation. I just can't figure out the answer. Hope you can help me ^^ , please.
This is the image with the exercise:
I can't figure out a) and c)
At b) you just gotta derivate the F(x) and write the table of variation of the function. Seems easy. But the other ones.. idk
Much appreciated.

Please don't use that site, which is showing me inappropriate ads. Here is your image:



Think about what F(a) has to be.

 

[HallsofIvy]

By the "fundamental theorem or Calculus" f(t)= 3x^2- 4x+ 1. Integrating that from a to x gives x^2- 2x^2+ x- (a^3- 2a^2+ a) and we are told that is equal two x^2- 2x^2+ x+ a. We must have a^3- 2a^2+ a= a or a^3- 2a^2= a^2(a- 2)= 0. a= 0 or a= 2.

 

[tiberiuiurco]

By the "fundamental theorem or Calculus" f(t)= 3x^2- 4x+ 1. Integrating that from a to x gives x^2- 2x^2+ x- (a^3- 2a^2+ a) and we are told that is equal two x^2- 2x^2+ x+ a. We must have a^3- 2a^2+ a= a or a^3- 2a^2= a^2(a- 2)= 0. a= 0 or a= 2.

and since a!= 0 , then a = 2. Got it. Thanks !
What about c) ?