Answer:
P = 1162 W
E = 33 476 923 Joules
Explanation:
Hi, to calculate the total power hitting the panel we must integrate the power density P(x,y) inside the panel area, that is:
[tex]P = \int\limits^{x=1}_{x=-1} \int \limits^{y=1-x^4}_{y-0} {P(x,y)}\, dxdy\\[/tex]
First we integrate the y variable since is the dependent variable for the present problem.
[tex]P = 1000W\int\limits^{x=1}_{x=-1} {(y' - \frac{y'^3}{3})\limits^{y'=1-x^4}_{y'=0}} \, dx\\\\\\P= 1000W \int\limits^{x=1}_{x=-1} {(1-x^4 - \frac{(1-x^4)^3}{3})} \, dx[/tex]
The integral is pretty straigthfoward, but involves expanding the binomial.
However the answer is:
[tex]P = 1000W \frac{1}{3} (\frac{x^{13} }{13} - \frac{x^{-9}}{3} +2x)\limits^{x=1}_{x=-1}\\\\P = 1000 \frac{136}{117} W[/tex]
That is:
P = 1162 W
Since 1W = 1J/1s
The total energy recieved in 8 hours will be:
E = P*(8*3600 s)
E = 33 476 923 Joules
