Which mathematical expression gives the total charge that passes through a wire…

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Which mathematical expression gives the total charge

\Delta q

that passes through a wire during the time interval from

t=0

t=T

when the current varies with time as

I(t)

? (a)

\displaystyle \Delta q = T\,I(0)

(b)

\displaystyle \Delta q = \dfrac{I(0)+I(T)}{2}\,T

(c)

\displaystyle \Delta q = \int_{0}^{T} I(t)\,dt

(d)

\displaystyle \Delta q = \int_{0}^{T} t\,\dfrac{dI}{dt}\,dt