integral calculus

[calculus]

if vC(t) = 1/C integral i(t)dt; with upper limit = t, lower limit = -infinity; if C= 0.001, i(t) = sin (1000 * 2PI * t), How to define vC(t)? I obtained the answer as vC(t) = 1000*t*sin(2000*Pi*t), can I checked it with someone?

 

[Deleted member 4993]

if vC(t) = 1/C integral i(t)dt; with upper limit = t, lower limit = -infinity;

if C= 0.001, i(t) = sin (1000 * 2PI * t),

How to define vC(t)? I obtained the answer as vC(t) = 1000*t*sin(2000*Pi*t), can I checked it with someone?

Do those Cs refer to the same parameter?

 

[HallsofIvy]

No, that is not correct. The anti-derivative of sin(1000*2pi*t) is -1/(2000 pi) cos(1000*2pi*t). There is no "t" multiplying it. And evaluating it at the upper limit "t" does NOT just multiply it by t- it is just the cosine evaluated at t. (That confusion is one reason it is not a good idea to use the same symbol for both the variable of integration and a limit of integration.)

The real problem is that you cannot evaluate the anti-derivative at "- infinity" even as a limit.