Calculating Jon's Energy Needs for First Week of Weight Gain Program

[385sk117]

Homework Statement

Jon needs to bulk-up for next AFL season. His energy needs t days after starting his weight gain program are given by E(t) = 350(80 + 0.15t)^0.8 - 120(80 + 0.15t) calcories/day. Find Jon's total energy needs over the first week of the program.

Homework Equations

The Attempt at a Solution

I integrated the fuction above and interval was [0, 7] as the question says total energy needs over the first week. The answer i got was 14377 but the answer is 14400.
I think there is some problem with the interval or the value of C which i couldn't find.
Help me please~

 

[HallsofIvy]

There is no "C" in this problem. What do you mean by that? If it were me, I wouldn't integrate. Since you are give "calories per day" and days are discreet quantities, I would just add E(0)+ E(1)+ E(2)+ E(3)+ E(4)+ E(5)+ E(6). Since E(7) is the calories needed after 7 days, it is not included in the calories consumed in the first 7 days.

 

[385sk117]

14378 is the answer i got from your method. And this question was under the heading of Integration so i think i should use integration method to solve it.