Answer:
Family will save 3600 gallons of water by replacing the shower-heads.
Step-by-step explanation:
Number of family members in a family = 5
Each member of the family averages shower per day = 8 minutes
Total time for shower = 5×8 = 40 minutes
With a 5 gallon shower-heads each member will use water in a day = 5×40 = 200 gallons
Water consumption in 30 days = 200×30 = 6000 gallons per month
After replacing the shower-heads with 2 gallons per minute shower-heads family will use the amount of water = 40×2= 80 gallons per day
Water used in one month = 80×30 = 2400 gallons
Now water save by the family in 30-day period = 6000 - 2400 = 3600 gallons
Therefore, family will use 3600 gallons less water by replacing the water saving water heads.
It looks like you're given

Then by the additivity of definite integrals this is the same as

(presumably this is what the hint suggests to use)
Then by the fundamental theorem of calculus, we have

For this case we must pose a verbal problem equivalent to the following expression:

So, we have:
The sum of double a number plus five.
We propose the expression:
A number subtracted from the sum of double the same number plus five equals twenty-six.
Answer:
A number subtracted from the sum of double the same number plus five equals twenty-six.