Over a interval

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Over a

10\text{ s}

interval, two electric currents

I_1(t)

and

I_2(t)

flow through a circuit. It is known that

\displaystyle\int_{0}^{10} I_1(t)\,dt = 12\text{ C}

and

\displaystyle\int_{0}^{10} I_2(t)\,dt = -4\text{ C}

. The net charge transferred during the interval is defined as

Q=\displaystyle\int_{0}^{10}\bigl(I_1(t)+0.5\,I_2(t)\bigr)\,dt

. Determine

Q