The rate of sales of a certain brand of bicycle by a retailer in thousands of do

Question

The rate of sales of a certain brand of bicycle by a retailer in thousands of dollars per month is given by

d/dt S(t) = 25t-0.42t^2 where t is the number of months after an advertising campaign has begun.

(a) Find the amount of sales, in thousand of dollars, for the first five months after the start of the advertising campaign. Give you answer to three decimal places.

$??? thousand dollars

(b) Find the average sales per month for the second five month period of the advertising campaign. Give you answer to three decimal places.

$ ??? thousand dollars per month

Please show me how to work it out.. I assumed for a it would be integral of S(t) from 5 to 10 ??

please help explanations please!

Explanation / Answer

Integrating 25t-0.42t2

25t2/2-0.42t3/3+c

put limits from t=0 to t=5 for first 5 months we get,

25*25/2 - 0.42*125/3 - 0=312.5-17.5=295

Total sales in next 5 months can be found by putting limits from t=5 to t=10

25*100/2-0.42*1000/3 - 295 =1250-140-295=815

aVERAGE SALES=815/5 = 163

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