Calculating Energy Expenditure in a Circuit Analysis Problem

[J.live]

The power supplied by a certain battery is constant 6 W over the first 5 mins, zero for the following two minutes, a value that increases linearly from zero to 20 W during the next 10 minutes, and a power that linearly decreases 20 W to zero in the following 7 minutes. What is the total energy in joules expended during this 24-minute interval?

P.S I know we have to solve for the area under the curve. We will be using E= W*T but i get lost where the value increases from zero to 20W and decreases back from 20W to zero. Any help will be appreciated.

 

[mplayer]

You are right about having to find the total area under the curve to solve for the total energy expenditure. One way you could deal with the calculation is to draw out the graph in full with time on the x-axis (in seconds) and power on the y-axis (in watts). When the power is increasing linearly from 0 to 20 W over the time interval from 7 to 17 minutes, this will form a triangle on your graph, and you can easily calculate the area it encloses. Same for the linearly decreasing part, the triangle it forms will just be of different dimensions. Hope that helps.

 

[J.live]

That did the trick, thank you!