A persons metabolic rate tends to go up after eating a meal...

A person's metabolic rate tends to go up after eating a meal and then, after some time has passed, it returns to a resting metabolic rate. This phenomenon is known as the thermic effect of food, and the effect (in kJ per hour) for one individual is F(t) = -10.8 + 172.8te^(-t/1.1), where t is the number of hours that have elapsed since eating a meal. Find the total thermic energy of a meal for the next five hours after a meal by integrating the thermic effect function between t = 0 and t = 5. The total thermic energy is about nothing kJ. (Round to the nearest whole number as needed.)

Transcript

00:01 Hi there, so for this problem, we are given the thermic effect of food for one individual, and that's given by the following expression, that is, that f of d is equal to minus 10 .8, this plus 172 .8 times the time, this times the aspect.

00:31 The nmptial of minus the time divided by 1 .1.

00:37 So what we need to determine is the integral of this function, integrated over the time, this from 0 to 5.

00:50 So that will be, we just substitute the expression that we are given, minus 10 .8 plus 172 .8 times, the time, this times the exponential of minus the time divided by 1 .1.

01:06 This integrated over the time.

01:09 So with that set, we just need to solve this integral.

01:14 So i'm going to separate this into two integrals.

01:17 The first one is the integral from 0 to 5 of minus 10 .8 integrated over the time.

01:23 So we can take out the constant that is minus 10 .8 and then just simply this reduces to the integral.

01:32 From 0 to 5 of the differential in time.

01:36 So we know that the solution of that integral is just the time.

01:40 This evaluated from 0 to 5.

01:43 So that will be minus 10 .8 times 5.

01:48 This will give us a value of minus 54.

01:59 So that's a solution for the first integral.

02:02 Now the second integral is, it's not that easy to solve because we will have zero to five.

02:13 Well, let me just take out the constant from this, which is my, well, it's positive, and that is 172 .8, and that the integral from zero to five of the time times the exponential of minus the time divided by 1 .1 is integrated over the time.

02:43 So with that said, we will have, we can just use their integration by parts to solve this integral.

02:54 So that will be that u is equal to the time, and then the differential in u is equal to the differential in time.

03:01 Now b, we choose, well, the differential in b is going to be the exponential of minus the time divided by 1 .1.

03:11 Then integrated both sides of this expression is that b is equal to minus 1 .1 times the exponential of minus the time divided by 1 .1.

03:23 Okay, so now, with that said, we will have 172 .8 this times, um, okay, so the first term in here by using the integration by parts is u times b.

03:43 So that will be minus 1 .1 times the exponential of minus the time divided by 1 .1...

Question

Please give Ace some feedback