Find average profit from q=0 to q=100

Question

p(q)= 396q - 2.1q^2-400 , find the average profit from q=0 to q=100 analytically

Answer 1

I write I[a,b] for the integral from a to b and E[a,b] for the evaluation from a to b

1/100 I[0,100] 396q - 2.1q² -400 dq = 1/100 E[0,100] 198q2 - .7q3 - 400q = 1/100 (198*100² - .7*100³ - 400 * 100) = (198*100 - .7*100² - 400) = 19800 - 7000 - 400 = 12400