Asolar panel occupies the region bounded by y = 1 − x^4 and y = 0 (length units in meters). suppose the power density of sunlight hitting the panel is p(x, y) = 1000 (1 − y/2) watts/m2 . find the total power hitting the panel. how much energy (joules) does the panel receive in 8 hours? (1 watt = 1 joule/sec)

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:

First we integrate the y variable since is the dependent variable for the present problem.

The integral is pretty straigthfoward, but involves expanding the binomial.

However the answer is:

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

answer; i believe the correct answer is (40,000 j) good luck

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