Power and energy delivered to a circuit element with exponential V and i

[mba444]

Homework Statement

2. The voltage and current at the terminals of the circuit element in Fig. 1 are zero for t<0. For t>0 they are

V= e^(-500*t)-e^(-1500*t) V
i= 30-40e^(-500*t)+10e^(-1500*t) mA

a) Find the power at t = 1 ms.
b) How much energy is delivered to the circuit element between 0 and 1 ms?
c) Find the total energy delivered to the element.

Figure 1. An ideal basic circuit element

Homework Equations

P=V*i
W=integral (P dt)

The Attempt at a Solution

i solved part a by simple substituting the time in both V and i equations then i multipled them giving me a result of 3.1 W, in the second part i used the integral where i substitued the answer i got in the previous part and set the integral to be from 0 to 1 ms but it turns to be wrong !

need your help tanx in advance

 

[CEL]

Homework Statement

2. The voltage and current at the terminals of the circuit element in Fig. 1 are zero for t<0. For t>0 they are

V= e^(-500*t)-e^(-1500*t) V
i= 30-40e^(-500*t)+10e^(-1500*t) mA

a) Find the power at t = 1 ms.
b) How much energy is delivered to the circuit element between 0 and 1 ms?
c) Find the total energy delivered to the element.

Figure 1. An ideal basic circuit element

Homework Equations

P=V*i
W=integral (P dt)

The Attempt at a Solution

i solved part a by simple substituting the time in both V and i equations then i multipled them giving me a result of 3.1 W, in the second part i used the integral where i substitued the answer i got in the previous part and set the integral to be from 0 to 1 ms but it turns to be wrong !

need your help tanx in advance

Voltage and current are variable and so is their product, the power. You must perform the multiplication and integrate it.

 

[mba444]

i did so as you said but i got a negative wrong answer

can you explain more in depth

 

[Redbelly98]

i did so as you said but i got a negative wrong answer

can you explain more in depth

If you show your work, somebody can help figure out where things went wrong.

 

[CEL]

i did so as you said but i got a negative wrong answer

can you explain more in depth

Both voltage and current start with the value 0 at t=0 and them they become positive. The current rises monotonically to 40 and after some time (well after 1 ms) the voltage starts to decay to zero, but still positive.
It is not possible that their product can be negative.