The current in amps through a resistor with a resistance of 90 Ohm varies according to I=2.8e^(−7.6t) when t is in seconds. What is the total energy dissipated in the resistor from 0.5 to 1.4 seconds, written in Joules?
The Attempt at a Solution
So I've tried writing it as dQ=2.8e^(−7.6t)dt and integrating from 0.5 to 1.4 seconds to find dQ. Then squaring that and dividing by (1.4-0.5)^2 to find I^2 and then P=R*I^2 and then U=P*dt. I'm not sure if there is a way I can use dQ directly to find dU. Actually I did just try rewriting the second equation as dU=dQ*(dQ/dt)*R and I got the same number, 0.006778 J which does seem pretty small