Question

Hello, I need that someone help me with this excersise.
I have to calculate (USING INTEGRATION) the motion ecuation of a particle. The excersise give me the ecuation of the velocity that is v=14t-32 , the initial time
t1=3

And the initial position of the particle:
X1=25
My first try was this

dx/dt = 14t-32
dx=(14t-32)dt

then I used defined integrals:

Int (dx) from 25 to x= int (14t-32 dt)from 3 to t

But when I resolved and then calculated it gave me this:

X-25=7 (t-3)^2-32 (t-3)+25
X=7 (t-3)^2 -32 (t-3)+25

And this is not the answer
I know that it could be calculated using:
x=X1+V1t+at
BUT I have to use calculus to resolver it.
Where's my mistake?
How do I have to integrate?
Please help me
Note: Don't forget that I HAVE TO USE INTEGRATION

Answer 1

dx = (14 t - 32) dt

x = 7 t^2 - 32 t + c

25 = 7 (3^2) - 32 (3) + c

25 = 63 - 96 + c ... 58 = c

x = 7 t^2 - 32 t + 58