If $h ^ { t }$ is a child's rate of growth in pounds per year, which of the following expressions represents the increase in the child's weight (in pounds) between the years 3 and 7 ?
A) $\int _ { 3 } ^ { 7 } h ^ { t } ( t ) d t$
B) $h ^ { t} ( 7 ) - h ^ { t } ( 3 )$
C) $\int _ { 7 } ^ { 3 } h ( t ) d t$

Question

Quizplus · Accepted Answer

The definite integral $\int _ { 3 } ^ { 7 } h ^ { t } ( t ) d t$ represents the area under the curve of the child's rate of growth function between the years 3 and 7, which gives us the total increase in weight during that time period. Option B gives us the child's rate of growth at years 3 and 7, but does not tell us how much weight was gained in between. Option C is the reverse of option A and gives us the negative of the correct answer.

If hth ^ { t }ht Is a Child's Rate of Growth in Pounds Per Year

If $h ^ { t }$ Is a Child's Rate of Growth in Pounds Per Year